How many years will it take $2,000 to grow to $3,300 if it is invested at 4.75% compounded​ continuously?

Answers

Answer 1

Answer:

10.54263764

Step-by-step explanation:

[tex]3300=2000e^{.0475t}\\\\1.65=e^{.0475t}\\\ln(1.65)=.0475t\\.500775288=.0475t\\t=10.54263764[/tex]

Answer 2

Answer:

It will take about 10.5 years for the investment to reach $3,300.

Step-by-step explanation:

Continuous compound is given by:

[tex]\displaystyle A=Pe^{rt}[/tex]

Where P is the principal, e is Euler's number, r is the rate, and t is the time (in this case in years).

Since our principal is $2,000 at a rate of 4.75% or 0.0475, our equation is:

[tex]\displaystyle A=2000e^{0.0475t}[/tex]

We want to find the number of years it will take for our investment to reach $3,300. So, substitute 3300 for A and solve for t:

[tex]3300=2000e^{0.0475t}[/tex]

Divide both sides by 2000:

[tex]\displaystyle e^{0.0475t}=\frac{33}{20}[/tex]

We can take the natural log of both sides:

[tex]\displaystyle 0.0475t=\ln\left(\frac{33}{20}\right)[/tex]

Therefore:

[tex]\displaystyle t=\frac{1}{0.0475}\ln\left(\frac{33}{20}\right)\approx 10.54\text{ years}[/tex]

It will take about 10.5 years for the investment to reach $3,300.


Related Questions

if 3/4 of a number is added to 5/4 it gives the same result as taking 7/8 of the number from 20 ⅓. Find the number​

Answers

Given:

[tex]\dfrac{3}{4}[/tex] of a number is added to [tex]\dfrac{5}{4}[/tex] it gives the same result as taking [tex]\dfrac{7}{8}[/tex] of the number from [tex]20\dfrac{1}{3}[/tex].

To find:

The unknown number.

Solution:

Let x be the unknown number.

[tex]\dfrac{3}{4}[/tex] of a number is added to [tex]\dfrac{5}{4}[/tex] it gives the same result as taking [tex]\dfrac{7}{8}[/tex] of the number from [tex]20\dfrac{1}{3}[/tex].

[tex]\dfrac{5}{4}+\dfrac{3}{4}x=20\dfrac{1}{3}-\dfrac{7}{8}x[/tex]

[tex]\dfrac{5+3x}{4}=\dfrac{61}{3}-\dfrac{7}{8}x[/tex]

[tex]\dfrac{5+3x}{4}=\dfrac{488-21x}{24}[/tex]

Multiply both sides by 24.

[tex]6(5+3x)=488-21x[/tex]

[tex]30+18x=488-21x[/tex]

[tex]18x+21x=488-30[/tex]

[tex]39x=458[/tex]

Divide both sides by 39.

[tex]x=\dfrac{458}{39}[/tex]

Therefore, the required number is [tex]\dfrac{458}{39}[/tex].

Please help with (ii). thank you!!!

Answers

Answer:

Exact surface area = 500+20pi square cm

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

Explanation:

A = area of the bottom face = 10*12 = 120B = area of the left face = 7*12 = 84C = area of the right face = 7*12 = 84D = area of the front face = 7*10-0.5*pi*2^2 = 70 - 2piE = area of the back face = 7*10-0.5*pi*2^2 = 70 - 2piF = area of the top face = 2*3*12+0.5*2*pi*2*12 = 72+24pi

All areas mentioned are in square cm, which can be abbreviated to cm^2.

Faces A,B,C are straight forward as they are simply rectangles. The remaining 3 other faces are a bit tricky.

Faces D and E involve subtracting off the area of a semicircle of radius 2 from a 7 by 10 rectangle area. The formula pi*r^2 is the area of a full circle, while 0.5*pi*r^2 is the area of a semicircle. From there, I then plugged in r = 2.

The top face is really a combination of 3 different pieces (two flat, one curved in the middle). Each flat part is of area 3*12 = 36, so that doubles to 2*3*12 when accounting for both flat parts. The curved portion will involve the lateral surface area of a cylinder formula which is

LSA = 2*pi*r*h

but since we're only dealing with half the lateral area, we multiply that by 0.5 to get 0.5*2*pi*r*h. From there, I plugged in r = 2 and h = 12.

-----------------------

In summary we have these six areas for the faces

bottom = 120left = 84right = 84front = 70 - 2piback = 70 - 2pitop = 72 + 24pi

Add up those sub areas to get the full surface area of this particular 3D solid.

120+84+84+(70-2pi)+(70-2pi)+(72+24pi)

(120+84+84+70+70+72)+(-2pi-2pi+24pi)

500+20pi

This is the exact surface area in terms of pi. If you want the approximate version of this, then you could replace pi with 3.14 and compute to get 562.8 cm^2

Use more decimal digits in pi to get a more accurate value. If you use your calculators version of pi, then you should get somewhere around 562.831853 cm^2

In this case, I think it's better to stick with the exact surface area (unless your teacher instructs otherwise).

please help i don’t have much time left !!!

Answers

Answer:

8.5

Step-by-step explanation:

QR is 10

PQRS AREA is 45

10 times 4.5 is 45

meaning BC and PQ is 4.5

4.5 plus 4.5 is 9

26 minus 9 is 17

17 divided by two is 8.5

AB is 8.5

1
What is the value of x in the equation x - y = 30, when y = 152
200

Answers

[tex]\displaystyle\bf 1) \ if\ y=152 \Longrightarrow x=30+152=182 \\\\2) \ if \ y =200 \Longrightarrow x=200+30=230\\\\3) \ if \ y=80 \Longrightarrow x=30+80=110\\\\4) \ if \ y=4 \Longrightarrow x=4+30=34 \\\\5)\ if \ y=8 \Longrightarrow x=30+8=38[/tex]

On a standard baseball field, consecutive bases are 90 feet apart. How far does the catcher have to throw the ball to get from home plate to 2nd base

Answers

I think the answer is 90 and the square root of 2, hope this helps

please help!!
The length of side AC is | 3,4,5,6 | units.
The area of triangle ABC is | 5,10,15,20 | square units.

Answers

Look at ∠A, the angle which resides on (1, 3). If we count 5 units down, you find the other endpoint on side AC. Hence, the length of side AC is 5 units. This figure is equal to the height of the graphed triangle.

If we mirror this process with the figure representing the triangle's length, side BC, we get 4 units.

The formula for calculating a triangle's area is [tex]\frac{1}{2}bh[/tex]. In this context, the base of the triangle is the same as the length. Now, let's plug in the base and the height.

[tex]\frac{1}{2}(4)[/tex] × [tex](5) = 10[/tex]

The area of triangle ABC is 10 squared units.

Answer:

first box: 5      second box: 10

Step-by-step explanation:

if demand is 75 lakh setup and holding cost is 29 and 35 number of piece per order is 2.3 lakh printing is done 300 days and delivery within 2 days what is eoq

Answers

A

64 :) i think

Step-by-step explanation:

Find a number such that if 16 is added to it, the ratio of the result to the original number is 4:3

Answers

Answer:

48

Step-by-step explanation:

let the number be x and x + 16 the result of adding 16 to it, then

the ratio of the result to the original is

[tex]\frac{x+16}{x}[/tex] = [tex]\frac{4}{3}[/tex] ( cross- multiply )

4x = 3(x + 16)  = 3x + 48 ( subtract 3x from both sides )

x = 48

Find an ordered pair to represent t in the equation t = u + v if u = (-1, 4) and v = (3, -2)

Answers

Given:

[tex]u=(-1,4)[/tex]

[tex]v=(3,-2)[/tex]

The equation is:

[tex]t=u+v[/tex]

To find:

The ordered pair to represent t in the given equation.

Solution:

We have,

[tex]t=u+v[/tex]

Substituting the given values, we get

[tex]t=(-1,4)+(3,-2)[/tex]

[tex]t=((-1)+3,4+(-2))[/tex]

[tex]t=(-1+3,4-2)[/tex]

[tex]t=(2,2)[/tex]

Therefore, the ordered pair to represent t in the given equation is (2,2).

someone PLS help me .. i believe this needs a quadratic formula?

Answers

Hello,

The parabola has vertex=(0,1) and is passing through (1,3)

y=k(x-0)²+1

3=k*1+1 ==> k= 2

y=2*x²+1

Is the number of hits to a website in a day a discrete random​ variable, a continuous random​ variable, or not a random​ variable?

Answers

Not a random variable.

Answer:

The random variable is discrete. :)

Step-by-step explanation:

a. 65
b. 67
c. 43
d. 23

Answers

The answer for this problem is a A.65

The three straight paths, , , and , meet each other at three points, A, B, and C. How do these points of intersection differ from each other? Explain the differences in terms of the angles that you see. Also look at the length of the side opposite each angle. What pattern do you see regarding the measurements? In what situation would all the points of intersection resemble one another? Modify the triangle in GeoGebra to help you with your answers

Answers

Answer:

Step-by-step explanation:

I am sort. I have no idea

Answer:

The three straight paths intersect at different angles. In other words, the amountrequired to turn one path onto the other is different about each vertex. Thelargest angle is opposite the longest side, and the smallest angle is opposite theshortest side. If all three points of intersection look the same, the result is atriangle with three equal angles and three equal sides.

Step-by-step explanation:

Which statement about these two restaurant meals is correct? A. Neither meal contains any nutrients. B. Meal A is the more healthful choice. C. Meal B is the more healthful choice. D. Both meals are healthful choices.​

Answers

Answer:

D. Both meals are healthful choices

Battle is making fruit baskets, which include apples and bananas to send to some of her real estate clients. She wants each basket to have at least 12 pieces of fruit but the fruit should weigh no more than 80 ounces total. On average each apple weighs 5 ounces and each banana weighs 7 ounces.

Answers

Answer:

there are 2 apples in the basket

there are 10 banana in the basket

Step-by-step explanation:

According to the Question,

We have, Battle is making fruit baskets, which include apples and bananas to send to some of her real estate clients. She wants each basket to have at least 12 pieces of fruit.

let x for apple And y for banana So, x+y=12---Equation 1

And, the fruit should weigh no more than 80 ounces total. On average each apple weighs 5 ounces and each banana weighs 7 ounces.

Thus, 5x+7y=80 ----Equation 2

Now, (Equation 1) × 5 Subtract with (Equation 2) We get,

2y = 20 ⇒ y=10 (there are 10 banana in basket)

Put value of y=10 in Equation 2 we get

5x+70=80 ⇔ x=2(there are 2 apples in basket)

instructions: state what additional information is required in order to know that the triangle in the image below are congruent for the reason given.

Given: AAS

Answers

Answer:

QP ≈ HG

Common side between those angles are QP and HG

so, they should be congruent to prove AAS

Answered by GAUTHMATH

the quantity of the square of the sum of 4 times
x and 3, divided by the difference of x and 10

Answers

Answer:

Step-by-step explanation:

(4x+3)²÷(x-10)

=(16x²+24x+9)÷(x-10)

x-10) 16x²+24x+9 (16x+184

       16x²-160x

       -      +

   ------------------

               184x+9

               184x-1840

              -      +

             ----------------

                       1849

              ----------------

       

Choose the smallest number. 3/18 10/3

Answers

Answer:

3/18

Step-by-step explanation:

3/18= 0.16

10/3= 3.33

Answer:

3/18

Step-by-step explanation:

3/18 , 10/3

Simplify it to the smallest size

3/18 , 10/3

1/6 , 10/3

1/6 = 3/18

Help me with this problem

Answers

6x=180
180/6 = 30
x = 30

Answer:

x = 30

Step-by-step explanation:

If A parallel to B , then

2x and 4x are same- side interior angles and sum to 180° , that is

2x + 4x = 180

6x = 180 ( divide both sides by 6 )

x = 30

What is the answer to 3/4 x 1/2

Answers

What is the answer to 3/4 x 1/2?

Answer : 0.375

Answer:

3/8

Step-by-step explanation:

50 pts pls help
What is the range of the function shown on the graph above?

Answers

572^ the answer above is correct!!!!!

Answer:

[0, 7]

Step-by-step explanation:

The range is the set of y-values.

The graphed function has its range between 0 and 7, both inclusive.

So the range is:

y ∈ [0, 7]

What is the recursive formula for this geometric sequence?
-3, -21, -147, -1029, ..

Answers

Answer:

b . is the answer

Step-by-step explanation:

ha ahhgahga

Write down five numbers so that:the mean is 6,the median is 5 and the mode is 4

Answers

Answer:

4 , 4 , 5 , 6 , 11

Step-by-step explanation:

Mode = 4

So at least two times 4 should be there in the data.

And median is 5. So the middle term ( 3rd term} should 5.

Let x and y be the 4th term and 5th term

Data set:

4 , 4 , 5 , x , y

Mean =6

[tex]\frac{4+4+5+x+y}{5}=6\\[/tex]

4+4+5 +x + y = 6*5

13 + x + y = 30

     x + y = 30 - 13

     x + y = 17

x ,y can be any numbers that sum up to 17.

x , y  can be  10 , 7   or  6, 11

Data set: 4 , 4 , 5 , 6, 11

Which property of math is the young student learning with the following equation? 3 x (4 + 7) = (3 x 4) + (3 x 7)

Answers

The property of math they are learning is the distributive property

If P=36 inches, find x and find the area

Answers

Answer:

x=4    Area = 56

Step-by-step explanation:

find x :

36 = 2 (3x + 2 + x)   (simplify)

36 = 2 (4x+2)           (divide both sides by 2)

18 = 4x + 2               (solve)

16 = 4x

4 = x

Find Area Substitute value of x

A= l × w

A = (3x + 2) × (x)

A = (3 × 4 + 2) × (4)

A = (12 + 2) × 4

A = 14 × 4  

A= 56

hope this helps :)

On a coordinate plane, a line goes through (negative 3, negative 4) and (3, 0).
What are the necessary criteria for a line to be perpendicular to the given line and have the same y-intercept?

The slope is Negative three-halves and contains the point (0, 2).
The slope is Negative two-thirds and contains the point (0, −2).
The slope is Three-halves and contains the point (0, 2).
The slope is Negative three-halves and contains the point (0, −2

Answers

Answer:

The slope is Negative three-halves and contains the point (0, 2).

Step-by-step explanation:

(-3,-4)(3,0)

M= -4/-6 = 2/3

⊥M = -3/2

0 = 2/3(3) + B

B=2

Can you help me with this question? It’s in the photo

Answers

Answer:

Option (d), (e) and (f) are correct.

Step-by-step explanation:

In triangle MNP, angle P = 90 degree

Cos M = 7 / 12

Now according to the right angle triangle

[tex]NP^2 = NM^2 - PM^2\\\\NP^2 = 12^2 - 7^2\\\\NP = \sqrt95[/tex]

Now

[tex]Sin M = \frac{sqrt95}{12}\\\\Cos N = \frac{95}{12}[/tex]

15< 4 + x
O A. x>11
O B. X> 19
O C. x< 19
O D. x< 11

Answers

Answer:

A. x>11

Step-by-step explanation:

15 < 4 + x

take 4 to the LHS this becomes 15 - 4 < x

•°• 11 < x

< means less than

Therefore x is greater than 11

x > 11

Carlos and Maria drove a total of 197 miles In 3.8 hours. Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the
remainder of the trip and averaged 47 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if
necessary.

Answers

Answer:

1.5 hours

Step-by-step explanation:

Carlos = x

Maria = y

55x + 47y = 197

x + y = 3.8

x = 3.8 - y

55(3.8 - y) + 47y = 197

209 - 55y + 47y = 197

-8y = -12

y = 3/2 = 1.5

what is the binary 11110-10101​

Answers

the binary is 1001 hope it helps
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