A population of mice is increasing exponentially. On Monday there were 120 mice. One month later there were 132 mice. Write a function to model this situation. Determine the percent increase of the population of mice each month.

Answers

Answer 1

Answer:

[tex]y =120*1.1^x[/tex]

[tex]r = 10\%[/tex] --- Percentage increase

Step-by-step explanation:

Given

Let

[tex]x \to months[/tex]

[tex]y \to mice[/tex]

So, we have:

[tex](x_1,y_1) = (0,120)[/tex] --- Monday

[tex](x_2,y_2) = (1,132)[/tex] --- One month later

Required

The function

The function is represented as:

[tex]y = ab^x[/tex]

In [tex](x_1,y_1) = (0,120)[/tex], we have:

[tex]120 =a * 1[/tex]

[tex]120 =a[/tex]

Rewrite as:

[tex]a = 120[/tex]

In [tex](x_2,y_2) = (1,132)[/tex], we have:

[tex]132 = a * b^1[/tex]

[tex]132 = a * b[/tex]

Substitute [tex]a = 120[/tex]

[tex]132 = 120 * b[/tex]

Solve for b

[tex]b = \frac{132}{120}[/tex]

[tex]b = 1.1[/tex]

Recall that:

[tex]y = ab^x[/tex]

Hence, the function is:

[tex]y =120*1.1^x[/tex]

To get the monthly percentage increase (r), we have:

[tex]y = a(1 + r)^x[/tex]

Compare to: [tex]y = ab^x[/tex]

So:

[tex]1+r =b[/tex]

Make r the subject

[tex]r = b-1[/tex]

[tex]r = 1.1-1[/tex]

[tex]r = 0.1[/tex]

Express as percentage

[tex]r = 0.1*100\%[/tex]

[tex]r = 10\%[/tex]


Related Questions

4,756 rounded to the nearest thousand is

Answers

4,756 rounded to the nearest thousand is 5,000.

Answer:

rounded to the nearest thousands 4,756 is 5,000 since 7 is higher then 4 so it rounds up

what is the value of the expression 6ab - b3 , if a=1 and b=2?

Answers

Answer:

6

Step-by-step explanation:

6(1×2) - 3(2)

6×2 - 6

12-6

= 6

here you go

please help with mine

please help me I will give brainlist​

Answers

Answer:

Option B

Step-by-step explanation:

I am sure

Hope this helped u

Answer:A

Step-by-step explanation:

picture, 20 points and will gibe brainliest..

Answers

Answer:

D : reflection over the y-axis followed by a translation to the right one unit

Select the correct answer from each drop-down menu.

Use the given functions represented by the equation and the graph to complete the statements.

f(x)=2x^3 - 3x^2 + 5x + 7

As x approaches positive infinity, f(x) approaches [negative infinity, positive infinity, zero] and g(x) approaches [negative infinity, positive infinity, zero]. The y-intercept of function f is [equal to, less than, greater than] the y-intercept of function g.

Answers

Answer:

f(x) approaches positive infinity.

g(x) approaches negative infinity.

the y-intercept of f(x) is less than the y-intercept of g(x).

Step-by-step explanation:

the highest power of x in f(x) is 3, and it has a positive sign. so, the bigger x the more the x³ part will dominate.

therefore, with x going to positive infinity, also f(x) goes to positive infinity.

the graph of g(x) clearly dives down never to come back up or flatten out. so, with x going to positive infinity, g(x) goes to negative infinity.

the y-intercept of f(x) = f(0).

that means the functional value when x=0.

so, for x=0 this means

y = 2×0³ - 3×0² + 5×0 + 7 = 7

the graph of g(x) shows that g(0) is 8.

so f(0) is less than g(0).

As x approaches positive infinity, f(x) approaches positive infinity and g(x) approaches negative infinity. The y-intercept of the function f is 7 and the y-intercept of function g is 8. #SPJ5

How to analyze the behavior of two given polynomials

Polynomials are algebraic expressions whose form is described below:

[tex]y = \sum \limits_{i = 0}^{n} c_{i}\cdot x^{i}[/tex]     (1)

Where [tex]c_{i}[/tex] is the i-th coefficient of the polynomial.

In this question we have two polynomials in two distinct presentations, an analytical and a graphical one, whose behaviors must be analyzed to fill the blanks of the paragraph given. The complete paragraph is shown below:

As x approaches positive infinity, f(x) approaches positive infinity and g(x) approaches negative infinity. The y-intercept of the function f is 7 and the y-intercept of function g is 8. #SPJ5

To learn more on polynomials, we kindly invite to check this: https://brainly.com/question/20121808 #SPJ5

I need help or my math teacher will call my parents up about it and I will die

Answers

Answer:

113mm^2

Step-by-step explanation:

Firstly work out the area of the pink circle using πr^2, which is the area of a process.

So we do πx12^2, which gives us 144π mm we have to divide this by two to get half of a circle hence giving us the area of the semi-circle. 72π mm is the area of the semicircle.

Then we must find the area of the white circle to subtract it from our semicircle. Since we know the radius is 12 from the center to anywhere, we know that the white circles diameter is 12, using our formula for the area all we need to do is πx6^2. This gives us 36π.

72π - 36π = 36π

36π is equal to 113.0973355 and since we need it too 3sf it will be 113mm^2

what is the length of the diagonal of the screen,in feet?

Answers

Answer:

12.2

Step-by-step explanation:

What are the amplitude and midline?

A. Amplitude: 1; midline: y = 1
B. Amplitude: 0; midline: y = 0
C. Amplitude: 2; midline: y = 1
D. Amplitude: 2; midline: y = 0

Answers

Answer:

A. Amplitude: 1; midline: y = 1

Answer:

A. Amplitude: 1; midline: y = 1

Step-by-step explanation:

i took the test

pls help me i don’t get this

Answers

Answer:

I think choose (c)

4x+1/x²-5

You want to buy the largest pizza in Northern Utah. You find a pizza that measures
75.36in around. What is the area that the pizza covers?

Answers

Answer:

451.7in^2

Step-by-step explanation:

You first need to determine the radius of the circle. This can be done by taking the circumference and dividing it by 2pi:

[tex]r=\frac{75.36in}{2\pi } = 11.99 in[/tex]

Now that you have the radius, you can plug it into the formula for the area of a circle (this is assuming the pizza is perfectly round):

[tex]A=\pi r^2=\pi (11.99^2)=451.7in^2[/tex]

The area that covers the circular pizza is: 451.64 in.²

What is the Area and Perimter of a Circle?

Area = πr²

Perimeter = 2πr, where r is the radius of the circle.

Given the following:

Perimeter of the circular pizza = 75.36 in.

Find the radius:

2πr = 75.36

r = 75.36/2π

r = 11.99 in.

Find the area:

Area = π(11.99)²

Area = 451.64 in.²

Learn more about the area of a circle on:

https://brainly.com/question/12269818

Someone please help me ASAP!

Answers

Answer:

x + 1 y+1

Step-by-step explanation:

it translated 1 unit up the x axis and 1 unit y axis

Answer:

reflected across the y-axis and translated 1 to the right and 1 up

Step-by-step explanation:

Please help me i need help ASAP!!! please help

Answers

Answers :

BC = 17.1

Angle B = 6.7°

Angle C = 83.3°

To find side BC, you use pythagorean’s theorem, which is a^2 + b^2 = c^2

This gives you 289 + 4 = 293, and you find the square root, which is 17.1.


To find the angle measures you can use tangent, which is opposite sides over adjacent sides. You plug these values into a calculator.

b = tan 2/17 = 6.7°

c = tan 17/2 = 83.3°



Answer:

BC = 17.1

m<B = 6.7 deg

m<C = 83.3 deg

Step-by-step explanation:

Find BC

a^2 + b^2 = c^2

AC^2 + AB^2 = BC^2

2^2 + 17^2 = BC^2

4 + 289 = BC^2

BC^2 = 293

BC = sqrt(293)

BC = 17.1

Find <B

tan B = opp/adj

tan B = 2/17

B = tan^-1 2/17

B = 6.7 deg

Find <C

m<A + m<B + m<C = 180

90 + 6.7 + m<C = 180

m<C = 180 - 90 - 6.7

m<C = 83.3

Which of the two functions below has the smallest minimum y-value?
f(x) = x5 - 2
g(x) = 3x2 + 1
A. The y-values for f(x)and g(x) both go to -
B. There is not enough information to determine
C. g(x)
O D. f(x)

Answers

Answer:

They have no minimum y -value

The minimum value for y belongs to f(x) at x=0 and function f(0)=(-2), Option D is correct.

The given function f(x)= x⁵-2

Differentiating the function we get,

5x⁴=0

x=0

Therefore, f(x)=f(0)=0-2=(-2)

Now function g(x)=3x²+1

Differentiating the function we get,

6x=0

x=0

Therefore, g(x)=g(0)=0+1=1

The minimum value for y belongs to f(x) at x=0 and f(0)=(-2)

To learn more on Functions click:

https://brainly.com/question/30721594

#SPJ7

PLSSSSS HELP MEEEE!!!!!!
Jose drove 35 miles in 2/3 hours. If he drove at a constant rate, how far did he travel in one hour? Enter your answer as a whole number, proper fraction, or mixed number in the simplest form.

Answers

Answer:

Jose traveled 52.5 miles in 1 hour

Step-by-step explanation:

What we're actually doing here is finding the "unit rate":  the speed in mph:

 35 mi       105 mi

------------ = ------------ = 52.5 mph = 52.5 miles in 1 hour

2/3 hr         2 hr

Jose traveled 52.5 miles in 1 hour

please answer thisss <3

Answers

Answer:

i think . it is c

Step-by-step explanation:

What is the radius of a hemisphere with a volume of 920 ft^3 to the nearest tenth of a foot?

Answers

Answer:

7.6 ft

Step-by-step explanation:

The volume of a sphere is

V = 4/3 pi r^3

A hemisphere is 1/2 of  a sphere

V = 1/2 (4/3 pi r^3)

V = 2/3 pi r^3

920 = 2/3 pi r^3

Multiply each side by 3/2

920 * 3/2 = 3/2 * 2/3 pi r^3

1380 = pi r^3

Divide each side by pi

1380/pi = pi r^3 / pi

1380/ pi = r^3

Using pi as 3.14

1380/3.14 = r^3

439.4904459= r^3

Taking the cube root of each side

(439.4904459)^(1/3)= r^3^(1/3)

7.602967711=r

To the nearest tenth

7.6 = r

radius=7.6ft

Answer:

Solution given:

radius [r]=?

Volume of hemisphere=920ft³

⅔*πr³=920

r³=920*3/(2π)

r³=439.267

r=[tex]\sqrt[3]{439.267}=7.6ft[/tex]

Darin has a rectangular vegetable garden. It is 5 yards long and 8 feet wide.
What is the perimeter of his vegetable garden? [best answer gets brainliest]

Answers

Answer:

about 15.328 yrds

Step-by-step explanation:

two sides are 5 yrds, so 5+5= 10yrds. two sides are 8 ft, 8+8=16 ft. there are .3333 yrds in 1 foot so 16*.3333 = about 5.328yrds

10+5.328 = 15.328

HELP! Drag each value to the correct location on the equation. Not all values will be used.
The number of archaeological sites discovered in a country over time, x, can be represented by the function S(x) = 2(1.1)x. The approximate number of artifacts found in each site over time, x, can be represented by the function A(x) = (1.1)5x + 2.

Create the function, T(x), that best describes the total number of artifacts found in archaeological sites in the country after x years.

Answers

Answer:

huh

Step-by-step explanation:

?

The exponential function that best describes the total number of artifacts found in archaeological sites in the country after x years = T(x) = [tex]2(1.1)^{6x+2}[/tex]

What is exponential function?

An exponential function is defined by the formula f(x) = a×, where the input variable x occurs as an exponent.

Time period = x years

The number of archaeological sites discovered in a country  in x years = S(x) = [tex]2(1.1)^{x}[/tex]

The approximate number of artifacts found in each site over time = A(x) = [tex](1.1)^{5x+2}[/tex]

The total number of artifacts found in archaeological sites in the country after x years = T(x) = S(x).A(x) = [tex]2(1.1)^{x}(1.1)^{5x+2} = 2(1.1)^{6x+2}[/tex]

Learn more about exponential function here

https://brainly.com/question/11487261

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if p (x) = 3x^3+2x^2+4x^4+3 and q (x) = 3x^4-2-x+5^2 .find p (x) - q (x)​

Answers

Answer:

4x⁴-3x⁴+5x³-3x²+1

Step-by-step explanation:

Given that p (x) = 3x^3+2x^2+4x^4+3 and q (x) = 3x^4-2-x+5x^2

p (x) - q (x)​ = 3x^3+2x^2+4x^4+3 - (3x^4-2-x+5x^2)

p (x) - q (x)​ = 3x^3+2x^2+4x^4+3 - 3x^4 + 2 + x - 5x^2

Collect the like terms

p (x) - q (x)​ = 4x⁴-3x⁴+3x³+2x²-5x²+x+3-2

p (x) - q (x)​  = 4x⁴-3x⁴+5x³-3x²+1

This givess the difference

Copy and Complete
A) price (increased or decreased) by %
B) price (increased or decreased( by %

Answers

Answer:

a) Price increased by 75%

b) Price decreased by 42.85%  (or 43% approximate)

Step-by-step explanation:

$ 40 increased by ____ % to $70

[tex]Percentage\ increase = \frac{difference}{ original} \times 100[/tex]

                             [tex]= \frac{70 - 40 }{40} \times 100\\\\=\frac{30}{40} \times 100\\\\= 75 \%[/tex]

$70 decreased by ______ % to $40

[tex]Percentage \ decrease = \frac{difference }{ original } \times 100[/tex]

                               [tex]= \frac{70 - 40 }{70} \times 100 \\\\= \frac{30}{70} \times 100\\\\=42.85 \%[/tex]

                       

One afternoon, Olive, who is 2 feet 3 inches tall, casts a shadow that is 6 feet 1 inch long. At the same time of
the day, a nearby tree casts a shadow that is 12 feet long. Olive reasons she can figure out the height of the
tree.
What is the height of the tree in feet? Round your answer to the nearest tenth of a foot.

Answers

2×12=24

24+3= 27

12*12=144

144/24=6

y=3x-1
Help pleaseeeeee

Answers

Answer:

y=3x-1

Step-by-step explanation:

Not enough context

Hope this helps!

:)

3. (16.03 LC)
A shape has 2 pairs of parallel sides and no right angles. What shape is it? (4 points)
A. Trapezoid
B. Parallelogram
C. Square
D. Rectangle

Answers

the answer is:
B. parallelogram

(i hope this is right)

A survey asked 25 students about their favorite sport. A frequency table of their responses is below.

Basketball
4.
Football
7
Lacrosse
3
Soccer
8
Volleyball
3

Which of the following is the correct relative frequency table for the students' favorite sport?

Basketball
0.16
Football
0.32
Lacrosse
0.12
Soccer
0.28
Volleyball
0.12

Basketball
0.16
Football
0.28
Lacrosse
0.12
Soccer
0.32
Volleyball
0.12

Basketball
0.04
Football
0.07
Lacrosse
0.03
Soccer
0.08
Volleyball
0.03

Basketball
4.
Football
7
Lacrosse
3
Soccer
8
Volleyball
3

Answers

Answer:

25.5 / 3 = 8.5

Step-by-step explanation:

8.5 times more student prefer basketball over soccer

Answer:

d

Step-by-step explanation:

If 2 is subtracted from 3 times a number , the result is 25.Find the number?

Answers

Answer:

3x-2=25

x=9. .

Answer:

9

Step-by-step explanation:

solve this simultaneous equation m+2n=10 and 2n+3m=18​

Answers

Answer:

m=4

n=3

Step-by-step explanation:

m+2n=10

2n+3m=18

Subtract

-2m=-8

m=4

Solve for n

(4)+2n=10

2n+3(4)=18

2n=10-4

2n=18-12

2n=6

n=3

What’s the answer (plz make sure it’s correct

Answers

Answer:

The first one is correct

Step-by-step explanation:

If both sides of the expression are equal, any number given as X would fit, meaning that there are infinitely many solutions.

Simplify the expression.

49 1/2 - 4 1/2

Answers

Answer:45

Step-by-step explanation:

49 1/2 - 4 1/2 = 45.....

HOPE IT HELPS!!

Dominic wants to find the distance between his house on one side of the park and his school on the other side. He marks off a third point forming a right triangle, as shown in the diagram. The distances in the diagram are measured in yards. Use the Pythagorean Theorem to find the distance from Dominic’s house to the school. Sho

Answers

Answer:

The distance from the house to the school is 500 units

Step-by-step explanation:

The distance we want to calculate represents the hypotenuse of the right triangle

So, to use the Pythagoras’ theorem, we need the two other side lengths apart from the hypotenuse

The base side measures (350-50 = 300 units)

The measure of the height is (450-50 = 400 units)

Mathematically, the theorem states that the square of the hypotenuse equals the sum of the squares of the two other sides

Thus, we have it that;

h^2 = 300^2 + 400^2

h^2 = 90,000 + 160,000

h^2 = 250,000

h = √250,000

h = 500 units

Can someone please help me

Answers

Answer:

28/43

Step-by-step explanation:

The question asks what is the probability that Marley picks out a blue or yellow marble.

In total, there are 43 marbles.

In total, there are 28 blue and yellow marbles. (18+10=28)

So, the answer would be 28/43

Hope this helps

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