Suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. Give the formula for calculating the size of that population after t years.

Answers

Answer 1

Answer:

y = 100(3)^t

Step-by-step explanation:

Use the formula y = P(1 + r)^t where y is the new amount, P is the starting amount, r is the rate as a decimal, and t is the time.

Plug in the values given:

y = 100(1 + 2)^t

y = 100(3)^t

Answer 2

Answer:

Step-by-step explanation:

y = 100(3)^t


Related Questions

...................................................

Answers

Answer:

11.21157846 =x

Step-by-step explanation:

We know log b (a) = c  can be written as b^c =a

log 3 (x) = 2.2

3^2.2 = x

11.21157846 =x

Answer:

[tex]\large \boxed{\sf \bold{A.} \ x=11.21}[/tex]

Step-by-step explanation:

[tex]\large \sf log_3 (x)=2.2[/tex]

Solve this by converting the logarithmic statement into its equivalent exponential form, using the relationship:

[tex]\large \sf log_b(y)=x[/tex]

[tex]\large{\sf y=b^x}[/tex]

Apply the relationship.

[tex]\large \sf log_3 (x)=2.2[/tex]

[tex]\large \sf x=3^{2.2}[/tex]

[tex]\large \sf x=11.21157845...[/tex]

[tex]\large \sf x \approx 11.21[/tex]

Please answer this question now

Answers

Answer:

Surface area of a cone = 461.58 In²

Step-by-step explanation:

Surface area of a cone = πrl + or

Surface area of a cone = πr(r+l)

Where r = radius

Radius= diameter/2

Radius=14/2

Radius= 7 inch

And l slant height= 14 inch

Surface area of a cone = πr(r+l)

Surface area of a cone = π*7(7+14)

Surface area of a cone = 7π(21)

Surface area of a cone = 147π

Surface area of a cone = 461.58 In²

write 1,245 in word form

Answers

Answer:

One thousand two hundred and forty five.

Hope this helps! (づ ̄3 ̄)づ╭❤~

Step-by-step explanation:


A shipping company borrows $70 million at 5% p.a. compound interest to build a new cruise ship. If it repays the debt after 3 years, how much interest will the company pay?

Answers

Answer:

about 11.03 million

Step-by-step explanation:

Use the equation I = P(1+r/100)^n - P (I is the compound interest, P is the principle, r is the rate percent, and n is the number of years):

Substitute the values given:

I = 70,000,000(1 + 5/100)^3 - 70,000,000

Use a calculator to solve and you will get ~11.03 million.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

The interest the company paid is $11 million.

What is compound interest?

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

P = $70 million

r = 5%

t = 3 years

n = 1

A = 70 ( 1 + 0.05)³

A = 70 ( 1.05)³

A = 70 x 1.05 x 1.05 x 1.05

A = $81 million

The amount of interest.

= A - P

= 81 - 70

= $11 million

Thus,.

The interest the company paid is $11 million.

Learn more about compound interest here:

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Find the area of the following rectilinear figure.

Answers

Answer:

Area : 14+10+40=64 square unit

Step-by-step explanation:

the area of the top rectangle with sides  2 and 7

A=2*7=14 square unit

the area of the middle rectangle with sides : (7-5)=2 and side (7-2)=5

Area=5*2=10 square unit

the bottom rectangle : sides 10 and 4

Area=10*4=40

add the areas : 14+10+40=64 square unit

5. Eight adults and six children travel in a cable car.
Estimate the total mass of the people in the cable car.​

Answers

Answer: 1880 pounds

Step-by-step explanation: when you take the average adult weight, around 160 lbs. you multiply that by eight. you get 1280. then you estimate that each of the children weigh around 100 lbs, then you add 600 to 1280 and get 1,880 lbs

△ABCis reflected to form​​ ​△A′B′C′​. The vertices of △ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of △A′B′C′ are A′(3, −1), B′(4, 2), and C′(6, −5). Which reflection results in the transformation of ​△ABC​​ to ​△A′B′C′​​? Reflection across the x-axis reflection across the y-axis reflection across y = x reflection across y=−x

Answers

Answer:

reflection across y = x

Step-by-step explanation:

Transformation is the movement of a point from its initial position to a new position. If a shape is transformed, all its point are also transformed. Types of transformation is reflection, rotation, transformation and dilation.

If a point is reflected across the x axis, the x coordinate is the same but the y coordinates is negated. If X(x, y) is reflected across the x axis the new point is X'(x, -y)

If a point is reflected across the y axis, the y coordinate is the same but the x coordinates is negated. If X(x, y) is reflected across the y axis the new point is X'(-x, y)

If a point is reflected across y = x, the x coordinate and y coordinates are interchanged. If X(x, y) is reflected across the y=x axis the new point is X'(y, x)

If a point is reflected across y = -x, the x coordinate and y coordinates are interchanged and both negated. If X(x, y) is reflected across the y=ix axis the new point is X'(-y, -x)

The vertices of △ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of △A′B′C′ are A′(3, −1), B′(4, 2), and C′(6, −5). The reflection of △ABC to form​​ ​△A′B′C′ shows a reflection across x axis since the x and y coordinates are interchanged

Answer:

reflection across y = x

Step-by-step explanation:

Given the sequence 4, 8, 16, 32, 64, ..., find the explicit formula. A. an=10(2n−1) B. an=5(2n−1) C. an=4(2n−1) D. an=20(2n−1)

Answers

Answer:

. an=4(2n−1)

Step-by-step explanation:

Identify the relation that is not a function. weight of an apple to the apple's cost time of day to the temperature at that time weight of a person to a person's height phone number to a person's name

Answers

Answer: Weight of a person to a person's height

Let x = weight and y = height. It is possible to have a certain weight correspond to multiple heights. This means the input x has multiple output y values. Therefore, we cannot have a function here. A function is only possible if for any x input, there is exactly one y output. The x value must be in the domain.

Find the term of each sequence.

32, 80, 200, ...5th term

Answers

Answer:

t5 = 1250

Step-by-step explanation:

Each term is derived by multiplying the previous term by 2.5

t2 = t1 * 2.5

t2 = 32 * 2.5

t2 = 80

===========

tn = a*b^(n - 1)

t3 = 32*2.5^2

t3 = 200

That's just to test the formula. It does work.

===============

t5 = 32*2.5^(5 -1)

t5 = 32*2.5^4

t5 = 1250

PLEASE HELP ME I GIVE 5 STARS !

Answers

Answer:

It's the 2nd option 2*2*3*3*5

Step-by-step explanation:

Answer:

b.

Step-by-step explanation:

you find a square root that goes into 180. i did 4 times 45. when you break apart 4 you get two times two. when you break apart 45 to get another square root, you get 9 times 5. when you break down 9 you get 3 and 3. so it is 2 times 2 times 3 times 3 times 5

Em um posto de combustível, o litro da gasolina estava custando R$2,40.Um cliente gastou R$72,00 para encher o tanque de seu carro. O valor do litro da gasolina sofreu 2 aumentos sucessivos,ambos de 10%. Quando o mesmo cliente gastara para encher o tanque do seu carro, após esees aumentos

Answers

Answer:

english i think u need hekp

A. 115
B. 167
C. 126
D. 96

Answers

Answer:

126

Step-by-step explanation:

Let x be the missing length

The triangles are similar:

● UE/140 = 45/x

From the graph we deduce that:

● UE = 140 - 90 = 50

Replace UE by its value

● 50/ 140 = 45/x

Switch x and 50

● x / 140 = 45/50

45/50 is 9/10 wich is 0.9

● x/140 = 0.9

Multiply 0.9 by 140

● x = 140 × 0.9

● x = 126

Answer:

I think its c 126

Step-by-step explanation:

Need help please! Oh and the options are
A. 2/3
B. 1/5
C. 4/15
D. 2/7

Answers

Answer:

C. 4/15There are 15 spaces in total with 4 shaded columns

Step-by-step explanation:

Answer:

Hey there!

The answer would be C. 4/15.

4/5(1/3)=4/15

Let me know if this helps :)

HELP ME PLZZzzzzzzzz​

Answers

Answer:

5 cm

Step-by-step explanation:

The volume (V) of milk in the container is calculated as

V = 8 × 15 × 12 = 480 cm³

After change of position with depth d then

8 × 15 × d = 480

120d = 480 ( divide both sides by 120 )

d = 4 cm

Find the exact value of cos A in simplest radical form.

Answers

Answer:

[tex] \cos(A) = \frac{2 \sqrt{6} }{7} [/tex]

Step-by-step explanation:

Since we are finding cos A we have

[tex] \cos(A) = \frac{AC}{AB} [/tex]

From the question

AC = √96

AB = 14

Substitute the values into the above formula

That's

[tex] \cos(A) = \frac{ \sqrt{96} }{14} [/tex]

We have the final answer as

[tex] \cos(A) = \frac{2 \sqrt{6} }{7} [/tex]

Hope this helps you

Waldnice!
8. I have a maximum/minimum thermometer in my greenhouse. It records the highest and
lowest temperatures reached since the time I reset it. I reset it on Sunday when the
temperature was 4°C. Overnight the temperature fell by 5°C. Then during Monday it rose by
6°C. before falling by 10°C during the night. On Tuesday it rose by 4°C and fell by 2°C
overnight.
What were the maximum and minimum temperatures recorded when I looked at the
thermometer on Wednesday morning?

Answers

Answer:

The maximum and minimum temperatures recorded by the thermometer when checked by Wednesday morning are 5°C and -5°C

Step-by-step explanation:

The given parameters are;

A maximum and minimum thermometer is used which records maximum and minimum values as follows;

Initial temperature on Sunday at the time of resetting the thermometer = 4°C

Temperature drop overnight = 5°C, new low = 4 - 5 =  -1°C,

Temperature rise on Monday = 6°C. New high = -1 + 6 = 5°C

Temperature drop on Monday night = 10°C. New low = 5 - 10 = -5°C

Temperature rise on Tuesday = 4°C = New high = 4 + - 5 = -1°C

Temperature drop on Tuesday night = 2°C. New low = -1 - 2 = -3°C

Therefore, the maximum and minimum temperatures recorded by the thermometer when checked by Wednesday morning are 5°C and -5°C.

The diagram shows 2 straight line , PQ and QR

Find the equation of QR

Help me to explain :) ​

Answers

Answer:

Step-by-step explanation:

We first need to find h. Since h is the x coordinate of Q, and Q is on the line 3x + 4y = 6, we will plug in the x value of h and the y value of 3 and solve for h:

3h + 4(3) = 6 and

3h + 12 = 6 and

3h = -6 so

h = -2

The coordinates for Q are (-2, 3). Now we can use that to find the slope of the line QR:

[tex]m=\frac{8-3}{3-(-2)}=\frac{5}{5}=1[/tex]

So the slope of QR is 1. Now we will choose one of the coordinates on line QR as our x and y coordinates to write the equation for the line in point slope form then in standard form:

y - 8 = 1(x - 3) and

y - 8 = x - 3 and

y - x = 5 or

-x + y = 5. If your teacher does not want you to lead with a negative:

x - y = -5 would be your equation in standard form.

Write each expression using a positive exponent. ("/" means division)("^" means to the power of) 9^-4

Answers

Answer:

Step-by-step explanation:

[tex]9^{-4}[/tex]

=[tex]\frac{1}{9^{4} }[/tex]                   ∴     [tex]x^{-n} = \frac{1}{x^{n} }[/tex]

=[tex]\frac{1}{9*9*9*9}[/tex]

=[tex]\frac{1}{6561}[/tex]

The product of (4z2 + 7z – 8) and (–z + 3) is –4z3 + z2 + z – 24.

Answers

The product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24

How to find product of expressions

(4z² + 7z – 8) and (–z + 3)

= -4z³+ 12z² - 7z² + 21z + 8z - 24

collect like terms

= -4z³ + 5z² + 29z - 24

Therefore, the product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24

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1 - Os coeficientes numéricos de uma equação do 2º grau (ax² + bx + c = 0), são números reais representados pelas letras “a, b e c”. Para que uma equação do 2º grau possa existir, é necessário que o coeficiente “a” seja DIFERENTE de: * 1 ponto a) -2 b) -1 c) 0 d) 1 2) Usando o método de Tentativa e Erro, visto na aula, qual das alternativas abaixo representa uma raiz da equação: x²-5x+6=0 * 1 ponto a) x = 0 b) x = 1 c) x = 2 c) x = -2

Answers

Answer:

1) La opción correcta es;

c) 0

2) La opción correcta es;

c) x = 2

Step-by-step explanation:

1) La forma general de una ecuación cuadrática se puede escribir en la forma;

a · x² + b · x + c = 0

Dónde;

a, y b son los coeficientes de x², x y c es el término constante

Por tanto, para que exista un polinomio de 2º grado es necesario que el coeficiente a sea diferente de 0

De lo que tenemos;

(0) × x² + b · x + c = 0, lo que da;

(0) × x² + b · x + c = b · x + c = 0 que es una ecuación lineal o un polinomio de primer grado

Por tanto, la opción correcta es c) 0

2)

La ecuación dada se presenta como sigue;

f (x) = x² - 5 · x + 6 = 0

Usando el método de prueba y error, tenemos;

Cuando x = 0

f (0) = 0² - 5 · (0) + 6 = 6 que no es igual a 0 y, por lo tanto, no es una solución

Cuando x = 1

f (1) = (1) ² - 5 · (1) + 6 = 1 que no es igual a 0 y por lo tanto, no es una solución

Cuando x = 2

f (2) = (2) ² - 5 · (2) + 6 = 0 que es igual a 0 y por lo tanto, es una solución

Cuando x = -2

f (1) = (-2) ² - 5 × (-2) + 6 = 20 que no es igual a 0 y por lo tanto, no es una solución

Por tanto, la opción correcta es c) x = 2

find the perimeter of a square of length of 5cm​

Answers

Answer:

20cm

Step-by-step explanation:

If each side of the square = 5 cm, 5 cm times 4 sides = 20 cm.

Answer:

P=20cm

Step-by-step explanation:

To find the perimeter of a square, you just add all the four sides.

Because it says the sides are 5cm, and squares always have the same length, you just:

5+5+5+6=20cm

So, the perimeter of this square is 20cm.

Hope this helps, and have a nice day:)

Show that 12.34343434………………can be expressed in the form p/q​

Answers

Answer:

1222/99

Step-by-step explanation:

12.343434.. =

= 12.(34)

= 12 34/99

= (12*99+34)/99

= (1188+34)/99

= 1222/99

Write the equation 5x − 2y = 10 in the form y = mx + b. y equals start fraction five over two end fraction x minus 10 y equals start fraction five over two end fraction x minus five y equals start fraction five over two end fraction x plus five y equals negative start fraction five over two end fraction x minus five

Answers

Answer:

y = 5/2x - 5

Step-by-step explanation:

You have to rearrange the equation so that it is equal to y.

5x - 2y = 10

(5x - 2y) - 5x = -5x + 10

-2y = -5x + 10

(-2y)/-2 = (-5x)/-2 + (10)/-2

y = 5/2x - 5

Solve. 100+[12×{20−(10÷5)}]

Answers

2000. This means yes I am not home now baby I’m sorry baby I’m just

Answer:

316

Step-by-step explanation:

Samantha’s college runs on a trimester schedule so she receives a bill 3 times a year for tuition. Each trimester costs $1,450, and Samantha must complete 2 years of college to receive her degree. The average cost for books each trimester is $350. Approximately what will be the total cost for Samantha to get her degree?

Answers

Answer:

10800

Step-by-step explanation:

1 trimesters cost = 1450 + 350  $

2 year -> 6 trimester

1800$ x 6 = 10800 $

help..!!! Why do i ask so many questions

Answers

Answer:

Hey there!

-4/3-4/5

-20/15-12/15

-32/15

Let me know if this helps :)

Harmony earns a \$42{,}000$42,000dollar sign, 42, comma, 000 salary in the first year of her career. Each year, she gets a 4\%4%4, percent raise.
Which expression gives the total amount Harmony has earned in her first nnn years of her career?

Answers

Answer:

FV(n)=42,000(1.04)^n

Step-by-step explanation:

FV=PV(1+r/n)^nt

Where

FV=future value

PV=present value

r=interest rate

n=number of periods

t=time (years)

PV=42,000

r=4%=0.04

n=1

t=n

FV(n)=p(1+r/n)^nt

=42,000(1+0.04/1)^1*n

=420000(1+0.04)^n

=42,000(1.04)^n

FV(n)=42,000(1.04)^n

Answer:

42000(1-1.04^n/-0,04)

Step-by-step explanation:

Please help me with this

Answers

verifying, by putting [tex] \theta=60^{\circ}[/tex]

LHS≠RHS

hence the question is FALSE

SP=2x+3, and LN=5x−14. Find SP. A. 20 B. 86 C. 43 D. 50

Answers

Answer:

C

Step-by-step explanation:

A segment joining the midpoints of two sides of a triangle is half the length of the third side.

SP is a midline segment, thus

SP = [tex]\frac{1}{2}[/tex] LN , that is

2x + 3 = [tex]\frac{1}{2}[/tex] (5x - 14) ← multiply both sides by 2

4x + 6 = 5x - 14 ( subtract 4x from both sides )

6 = x - 14 ( add 14 to both sides )

20 = x

Thus

SP = 2x + 3 = 2(20) + 3 = 40 + 3 = 43 → C

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