Hector invests $20,000 at age 21. He hopes the investment will be worth $200,000 when he turns 40. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.

Answers

Answer 1

Answer:

12.12%

Step-by-step explanation:

We have that the formula is given by:

A = p * e ^ (r * t)

From here, we know that A = 200000; p = 20000 and the time we can calculate 40 - 21 = 19

if we replace we have:

200000 = 20000 * e ^ (19 * r)

we must calculate r:

e ^ (19 * r) = 200000/20000

e ^ (19 * r) = 10

19 * r = ln 10

r = ln 10/19

r = 0.1212

In other words, the rate of growth is 12.12%

Answer 2

Answer:

12.1%

Step-by-step explanation:


Related Questions

One brand of coffee is packaged in cylinders where the height is equal to the radius, r. The volume of the package, in cubic centimeters, can be found using the function V(r) = πr3. The number of ounces of coffee in the cylinder depends on the volume of the cylinder, V, in cubic centimeters. This can be modeled by the function C(V) = 3.2V. Which function can be used to find the number of ounces of coffee in the can based on its radius? C(V(r)) = 32.768πr3 C(V(r)) = 3.2πr3

Answers

Answer:

C(V(r)) = 3.2πr3

Step-by-step explanation:

This problem is a composition of function defined by C(V(r)), now we have the functions [tex]V(r)= \pi r^{3}[/tex] and [tex]C(V)=3.2V[/tex], where the first depends on the radius, and the second dependes on the volume, that means, to find the number of ounce of coffe, we need to determine the volume of the cylinder, that's why we have to replace the volume function inside the ounces function,

[tex]C(V(r))=3.2(\pi r^{3} )[/tex]

Therefore, the right answer is the last choice.

Solve |6k + 12| + 9=9 for k

Answers

|6k+12|=0
6k+12=0
K=12/6= -2 or 2

Answer:

k= -2

Step-by-step explanation:

Look at recent question

Answers

Answer:

ok was it college math if so the I don't know

The vertices of ΔDEF have coordinates D(–1, 2), E(3, 3), and F (2, –4).What are the coordinates of the vertices of r(90°, O)(ΔDEF)?

Answers

Answer:

D,E

Step-by-step explanation:

hope I helped

Ana has a rectangular garden with a width of 2.3 meters and a length of 2.8 meters. She makes the model below to help her determine the area of her garden. What is the area of Ana's garden?

Answers

Answer:

6.44 m2                                                                      

Step-by-step explanation:

What best determines whether a borrower’s interest rate on an adjustable rate loan goes up or down

Answers

Answer:

a market's condition

Step-by-step explanation:

edge 2021

Market conditions best determine whether a borrower’s interest rate on an adjustable rate loan goes up or down.

What is the interest rate?

It is the cost of borrowing money.

Interest rate levels depend on the supply and demand of the money.

Supply and demand are a part of market conditions.

We see that,

An increase in demand for money will increase the interest rate.

A decrease in demand for money will decrease the interest rate.

Conversely,

An increase in the supply of money will decrease the interest rate.

A decrease in the supply of money will increase the interest rate.

Demand and supply are market conditions

Thus market conditions best determine whether a borrower’s interest rate on an adjustable rate loan goes up or down.

Learn more about demand and supply in a market here:

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The sum of five consecutive integers is 70. What are the numbers?

Answers

Answer: The numbers are 12, 13, 14, 15, and 16.

Step-by-step explanation:

Write an algebraic equation.

x + (x+1) + (x+2) + (x+3) + (x+4) = 70

5x + 10 = 70

subtract 10 from both sides

5x = 60

divide each side by 5

x = 12

The numbers are 12, 13, 14, 15, and 16.

Answer:

12 to 16 :) hope it helped

Factorise 2y^2 + y + 6xy + 9x - 3​

Answers

Answer: (2y+3)(3x+y-1)

Step-by-step explanation:

First regroup the terms.

6xy+9x+2y^2+y-3

Second factor 3x out of 6xy+9x

3x(2y)+9x+2y^2+y-3

3x(2y)+3x(3)+2y^2+y-3

And you get

3x(2y+3)+2y^2+y-3

Third factor by grouping

Round 0.378 to the place underlined digit 3

Answers

Answer:

0.38

Step-by-step explanation:

7 is the 3rd digit, so 8 is greater then 5, so you round up, if it is correct, can you give brainiest

Answer:

0.40

Step-by-step explanation:

this is because the number before it is up to five and even more than 5 so we round it up by adding one to the next number and the remaining digit to zero

Distance between (-1,0) and (8,6)

Answers

Answer:

3 √ 13

Step-by-step explanation:

Answer:

3√13

Step-by-step explanation:

We want to find the distance between these two points. To do so, we need to use the distance formula which states that the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is:

d = [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]

Here, [tex]x_1=-1,x_2=8,y_1=0[/tex], and [tex]y_2=6[/tex]. So:

d = [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]

d = [tex]\sqrt{(-1-8)^2+(0-6)^2}=\sqrt{(-9)^2+(-6)^2} =\sqrt{81+36} =\sqrt{117} =3\sqrt{13}[/tex]

Thus, the answer is 3√13.

~ an aesthetics lover

The formula A=12(b+c)h. Write the equation in term of c?

Answers

Answer:

[tex]c = \frac{A}{12h} - b[/tex]

Step-by-step explanation:

Okay, so the goal is to isolate c on one side with all the other terms on the other side. So, let's start by dividing both sides with 12h. After we do that, we will be left with [tex]\frac{A}{12h} = b+c[/tex]. Now, we can subtract both sides by b, and we will be left with [tex]\frac{A}{12h} - b = c[/tex]. Yay! We've now isolated c and that is our final answer!

Hope this helped! :)

Which types of triangles can be formed by taking the cross-section of a rectangular prism like the one shown above?

Answers

Answer: Equilateral, isosceles and scalene.

Step-by-step explanation:

Tell the measure of the angles In degrees 1/4

Answers

Answer:

so 1/4 of a circle is 90 degrees 1/4 is equal to 90 over 360 C it's 90 parts of 360. so here we go with this one. this angle is 20 degrees remember that's 90 alright the square one and this little part would be 20 degrees each angle appears wider as the Rays get longer.

Step-by-step explanation:

Let me know if this help's you lol :)

The measure of 1/4 is 90°

Two forces are acting on an object at the same point. Determine the angle between the two forces. (-2,7) and (3,-1)

Answers

The answer is 56 degree

Answer:

It is 124 degrees.

Step-by-step explanation:

You square each coordinate like this:

sqrt(x^2+y^2 )

You will end up getting sqrt(53 and sqrt(10.

Then find the dot product which is -6+-7=-13.

Then cos^-1(-13/sqrt53*sqrt10)

=124 degrees

Classify each representation shown below as either linear or exponential.

x y
0 5
1 7.5
2 11.25


y = 2x + 4



One person sends an email to 2 people. Those 2 people send it to 4 people, and those 4 send it to 8 people.



Answers

1. Exponential

2. Linear

3. Exponential

1.] What is the probability of choosing a king
from a standard deck of playing cards?

Answers

Answer:

1/13

Step-by-step explanation:

there are 4 kings in a deck of 52 cards.

4/52 = 1/13

12 divided by 9 tenths and hundredths

Answers

1.333 the answer I hope help

Which of the following statements is FALSE? The correlation coefficient equals the proportion of data points that lie on a straight line. The correlation coefficient will be +1.0 only if all the data lie on an upward-tilting straight line. The correlation coefficient is undefined if all the data lie on a perfectly horizontal straight line. The correlation coefficient is a unitless number and must always lie between –1.0 and +1.0, inclusive.

Answers

Answer:

The first one is False.

Step-by-step explanation:

If the correlation coefficient can also be -1 if the data lies on an upward tilting straight line.

an automobile traveled 21 miles north from the airport. it then turned directly west and traveled 28 miles. how far is the automobile from the airport??​

Answers

The automobile is 35 miles away from the airport

What’s the correct answer for this?

Answers

ANSWER: D

Isosceles Right Triangle has 3 angles: 90 degrees, 45 degrees and 45 degrees

Answer:

D

Step-by-step explanation:

It is isosceles (having two sides and angles congruent) and it is right will provide enough information to find all the angles of the triangles.

The states that dropped out of the Union, became the __________________ States of America 58 POINTS!!!

Answers

Answer:

Confederate

Step-by-step explanation:

During the time that led up to the conflict known as the Civil War of America, the major cause of tension was slavery. Southern plantation owners and farmers fiercely advocated slavery because they helped with the harvest of crops and the overall southern economy. The northerners, however, resisted slavery, saying it was immorally and inhumanely wrong.

At the culmination of this tension, many southern states, led by Jefferson Davis (who later became the "president" of the Confederate states), decided to secede from the Union (break away) and establish their own entity, which they called the "Confederate States of America".

A 6-sided die is rolled three times. What is the probability of rolling a 4 each time?
A 0.00463
B. 0.99537
C 0.16667
D. 0.00231

Answers

Answer:

a

Step-by-step explanation:

math

Which of the following are perfect squares? Check all that apply.

Answers

Answer: 16, 64, and 49

Step-by-step explanation: Perfect squares are products made by squaring or multiplying a whole number by itself twice.

11 is not a perfect square since nothing can

be multiplied by itself to give us 11.

The same is true for 62 and 15.

16 is a perfect square since it's possible to find a whole number that can be multiplied by itself to give us 16.

That number is 4 since 4 × 4 = 16.

64 is also one since 8 can be multiplied by itself twice to give us 64.

49 is also one since 7² or 7 × 7 is 49.

Answer:D,E and F

Step-by-step explanation:

Perfect squares are numbers in which their square roots are whole numbers.

From the options

√16 =4

√64 =8

√49 =7

Solve for x - y = -3

Answers

Answer:

0-3=-3

Step-by-step explanation:

What is x:
1. X-y= -3
2. Add y to both sides
3. X= -3+y

What is y:
1. X-y= -3
2. Subtract x from both sides
3. -y=-3-x
4. Divide both sides by negative 1
5. y=3+x

Solution;
-3+y, 3+x

Hope this helps!!

How many different 12-letter arrangements can be made using the letters in the word indianapolis?

Answers

Answer:

764

Step-by-step explanation:

A chessboard has 64 squares. George places 1 grain of rice on the first square, 2 grains on the second square, 4 grains on the third square, 8 grains on the fourth square, and so on, until he has placed grains of rice on 10 squares.
Once George has put rice on the 10th square, he has placed a total of _____ grains of rice on the chess board.

Answers

Hey there! I'm happy to help out!

As you can see, our number keeps on doubling. It's like 2×2×2×2.... so on and so forth. Whenever we multiply a number by itself, we can model it as an exponent, so if we had 2², it is two twos being multiplied, and 2×2=4. If it was 2³, it would be 2×2×2=8.

However, we have a one. This signifies a starting point and exponents have our back. Anything to the 0th power is always equal to one! So, this situation would look something like this:

[tex]2^0, 2^1, 2^2, 2^3,2^4,... etc.[/tex]

So, for the second square, we are going to the first power. For the fourth square it's going to the third power. Therefore, the 10th square will be the 9th power!

[tex]2^9=[/tex] 2×2×2×2×2×2×2×2×2= 512

However, we want to find how much he has done in total! So, let's find how much he did on the other squares!

[tex]2^8[/tex]= 256

[tex]2^7[/tex]=128

[tex]2^6[/tex]=64

[tex]2^5[/tex]=32

[tex]2^4[/tex]=16

2³=8

2²=4

[tex]2^1[/tex]=2

[tex]2^0[/tex]=1

Now, we add these all up to find the total grains of rice!

512+256+64+32+16+8+4+2+1=895

Therefore, George has placed a total of 895 grains of rice on the chess board.

I hope that this helps! Have a wonderful day!

Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.

What is a geometric sequence?

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

We have,

On the first square, George placed 1 grain of rice.

On the second square, he placed 2 grains.

On the third square, he placed 4 grains.

On the fourth square, he placed 8 grains.

In general, on the nth square, he places [tex]2^{n-1}[/tex] grains.

So,

On the first 10 squares,

1 + 2 + 4 + 8 + ... + [tex]2^9[/tex]

This is a geometric series with a first term of 1 and a common ratio of 2.

The sum of the first n terms of a geometric series.

[tex]S_n[/tex] =[tex]a(1 - r^n) / (1 - r)[/tex]

where a is the first term, r is the common ratio, and n is the number of terms.

Substituting the values,

[tex]S_{10}[/tex] = 1(1 - 2^10) / (1 - 2)

    = 1(1 - 1024) / (-1)

    = 1023

Therefore,

Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.

Learn more about geometric sequence here:

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Solve for a,b,and/or c
Help solve ASAP!

Answers

Answer:

a=90-67=23°

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

The (average) sales price for single family property in Seattle and Port Townsend is tabulated below.



Year Seattle Port Townsend


1970 $38,000 $8,400


1990 $175,000 $168,400



Find a linear model relating the year x and the sales price y for a single family property in Seattle.

Answers

Answer:

[tex]y=6,850x - 13,456,500[/tex]

Step-by-step explanation:

To find the linear model, we need to find a linear equation, where its slope is defined as

[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

So, we use the given points (1970, 38000) and (1990, 175000), to find the slope

[tex]m=\frac{175,000-38,000}{1990-1970}=\frac{137,000}{20} =6,850[/tex]

Now, we use the point-slope formula to find the equation

[tex]y-y_{1} =m(x-x_{1} )\\y-38000=6850(x-1970)\\y=6850x-13,494,500+38,000\\y=6,850x - 13,456,500[/tex]

Therefore, the linear model is

[tex]y=6,850x - 13,456,500[/tex]

A child is laying on the ground relaxing and looking up at a plane that is passing by. If the plane’s altitude is 33,500 feet and the child’s eyes are located 8,200 feet away from a point on the ground directly beneath the plane, what is the angle of elevation for the child’s line of sight to the plane?

Answers

Answer:

  about 76.2°

Step-by-step explanation:

The geometry can be modeled by a right triangle with the given dimensions being the side opposite the angle (height = 33,500 ft) and the side adjacent to the angle (8,200 ft). The fact that you know these two sides suggests the inverse of the tangent function may be useful.

  Tan = Opposite/Adjacent

  tan(angle) = (33,500/8,200)

  angle = arctan (335/82) ≈ 76.246°

The angle of elevation is about 76.2°.

How to find the area of the seating area

Answers

Parallelogram area is base times height.  Base of 14, height of 10,

Answer: A = (14 ft)(10 ft)    second choice

Answer:

choice B

Step-by-step explanation:

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