Suppose you deposit 900 dollars into a bank with 5% simple interest. The amount in the account after t years is given by A(t)=900(1.05)t (in dollars).
1. What is the average rate of change for the first year? Rate (in dollars per year): 900(1.05)-900
2. What is the average rate of change for the first five years? Rate (in dollars per year):
3. What is the average rate of change for the first ten years? Rate (in dollars per year):
4. Does the average rate of change increase or decrease as time from the initial deposit gets longer?

Answers

Answer 1

Answer:

1. 45 dollars per year.

2. 49.73 dollars per year.

3. 56.6 dollars per year.

4. Increases

Step-by-step explanation:

Average rate of change

The average rate of change of a function [tex]f(x)[/tex] over an interval [a,b] is given by:

[tex]A = \frac{f(b)-f(a)}{b-a}[/tex]

In this question, we have that:

[tex]A(t) = 900(1.05)^t[/tex]

1. What is the average rate of change for the first year?

[tex]A(0) = 900(1.05)^0 = 900[/tex]

[tex]A(1) = 900(1.05)^1 = 945[/tex]

So

[tex]A = \frac{A(1)-A(0)}{1-0} = \frac{945-900}{1-0} = 45[/tex]

45 dollars per year.

2. What is the average rate of change for the first five years?

[tex]A(0) = 900(1.05)^0 = 900[/tex]

[tex]A(5) = 900(1.05)^5 = 1148.65[/tex]

[tex]A = \frac{A(5)-A(0)}{5-0} = \frac{1148.65-900}{5-0} = 49.73[/tex]

49.73 dollars per year.

3. What is the average rate of change for the first ten years?

[tex]A(0) = 900(1.05)^0 = 900[/tex]

[tex]A(10) = 900(1.05)^{10} = 1466[/tex]

[tex]A = \frac{A(10)-A(0)}{10-0} = \frac{1466-900}{10-0} = 56.6[/tex]

56.6 dollars per year.

4. Does the average rate of change increase or decrease as time from the initial deposit gets longer?

From the previous items, it increases.


Related Questions

2/5 g = 3/5 help I don't know what the answer is

Answers

Answer:

Step-by-step explanation:

2/5 g = 3/5

g = 3/5 - 2/5 = 1/5

Evaluate f(4)  for the function f(x)=3x-5
A.12
B.7
C.9
D.17​

Answers

the answer is b.7

Step-by-step explanation:

because you have to plug in the f(4) to the equation like this

f(4)=3(4)-5

and then multiple 3x4 which is 12 then subtract 12 and 5 and you get 7.

3x^2+xy factorise it ​

Answers

Answer:

The factorized expression is [tex]x(3x + y)[/tex]

Step-by-step explanation:

We are given the following expression:

[tex]3x^2 + xy[/tex]

Factorizing:

We place the common factor in evidence.

The common factor of both elements of the sum is x. So

[tex]3x^2 + xy = x(\frac{3x^2}{x} + \frac{xy}{y}) = x(3x + y)[/tex]

The factorized expression is [tex]x(3x + y)[/tex]

Question 1b.
The distribution is...
i. Reasonably symmetric
ii. Abnormal
iii. Highly Skewed
iiii. Bimodel

Answers

Answer:  i) Reasonably symmetric

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

Explanation:

The data set is

35,40,45,49,51,54,57,58,58,64,68,68,75,77

Erase the outer pair of values (35 and 77) to end up with this smaller set

40,45,49,51,54,57,58,58,64,68,68,75

Repeat and erase off the outer values (40 and 75) to end up with

45,49,51,54,57,58,58,64,68,68

Keep going until we have either one or two elements left

49,51,54,57,58,58,64,6851,54,57,58,58,6454,57,58,5857,58

At this point, we see that the center is between these two last values. So the median is (57+58)/2 = 57.5

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

The center is at 57.5

Let L = {35,40,45,49,51,54,57} consist of the set of numbers lower than the median

Let U = {58,58,64,68,68,75,77} be the upper set of values larger than the median.

The middle of set L is 49 and the middle of set U is 68. So Q1 and Q3 are 49 and 68 respectively.

From that, we see the IQR = Q3 - Q1 = 68-49 = 19

Let A and B be the lower and upper fence

We would then say

A = Q1 - 1.5*IQR = 49-1.5*19 = 20.5

B = Q3 + 1.5*IQR = 68 + 1.5*19 = 96.5

Notice how all of the given data values are between A = 20.5 and B = 96.5, which means we don't have any outliers.

Furthermore, if we plotted a box-and-whisker plot (see below), we can see that the two whiskers are fairly the same length. It's not perfect but they're reasonably symmetric. Similarly, the median is somewhat in the middle of the box itself. So this gives a rough idea that the data set we're dealing with is fairly symmetric.

More confirmation can be in the form of a histogram which is also part of the image below. This histogram is fairly symmetric as the left half is nearly (not perfectly) a mirror image of the right half, and vice versa. No one side pulls too far out to create a highly skewed distribution.

Answer pls thank you

Answers

Answer:

I got 5.19.

Step-by-step explanation:

With this number there is no way to get a perfect sqaure. When you square root it, you get a decimal. If there's an option where it says no perfect square I'd suggest putting that

Please please help me I have to finish and on question 2

Answers

The answer is D


I’m pretty sure I hope it helped

Find the slope of the line that passes through the two points. (-3, -4), (6, 8)

Answers

Answer:

Step-by-step explanation:

let (x1 , y1) = ( - 3, - 4) and (x2 , y2) = ( 6 , 8)

Slope (m)

= y2 - y1 / x2 - x1

= 8 + 4 / 6 + 3

= 12 / 9

= 4/3

What is MA and ABC ifMB = 35° and MC equals 92°

Answers

Assuming is a triangle MA is 53°.

Explanation: the angles within a triangle can only make up 180° total. No other number. Since there is only three sides, ABC, I assumed it was a triangle. I added MB and MC to get 127. Subtracted 127 from 180, and got 53.

Two mechanics worked on a car. The first mechanic charged $55 per hour, and the second mechanic charged $90 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $1900. How long did each mechanic work?

Answers

55x+90y=1900
x+y=25, x=25-y
55(25-y)+90y=1900
1375-55y+90y=1900
35y=525
y=15
So it is 15 for the 90$ and 10 for the 55$

PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!

Answers

Answer: no solution

Step-by-step explanation:

They have the same slope which means they are parallel lines that will never cross or intersect. This mean that there is no solution

.A town fair charges $6 for general
admission and $1.50 for each ride. Use
the pattern in the table to find the cost of 7
rides and 10 rides. Then write an equation
for the pattern.

Answers

Answer: $1.50r + $6

Step-by-step explanation:

1.50 times 7 is $10.5 without admission

1.50 times 10 is $15 without admission

(R for rides)

so $1.50r + $6 is the equation

The following system of inequalities shows the relationship between two numbers, where the value of x is less than the value of y,
and both numbers are integers.


Which solution is valid within the context of the situation?

Answers

Answer:

(-1,5)

Step-by-step explanation:

An equilateral triangle has a side length of 10 units. What is its area?

Answers

Answer:

Hope my ans help you plz if u can mark me brainlist

Step-by-step explanation:

A = 43.3

The area of an equilateral triangle has a side length of 10 units is 43.3 square units.

What is an equilateral triangle?

An equilateral triangle is one with equally long sides on both sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. As a result, with each angle measuring 60 degrees, it is sometimes referred to as an equiangular triangle.

Given the side of an equilateral triangle  = 10 units

the area is given by,

A = √3/4 × a²

where a is the length of the side,

A = √3/4 × 10²

A = 1.732 x 100/4

A = 43.3 square units.

Therefore, the area of a triangle is 43.3 square units.

Learn more about equilateral triangle;

https://brainly.com/question/3461022

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please help 7m - 10 - 4m + 3

Answers

Step-by-step explanation:

7m - 10 - 4m + 3

3m-7

Hope it helps

7m-10-4m+3
=7m-4m-10+3
=3m-7

7. Richard deposited $5400 and got back an amount of $6000 after 2 years.
Find Richard's interest rate.

Answers

Answer:

600

Step-by-step explanation:

PLEASE HELP‼️‼️
A
B
C
D

Answers

Answer:

C i think

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

use the side splitter theorem

6/12 = x/18 (replacing AQ with x)

12x = 108 (cross multiply)

x = 9

ANYONE PLEASE JUST HELP ME I HAVE ASKED THE SAME QUESTION 3 TIME BUT NO ONE ANSWERS IT. I WILL GIVE BRAINLEST PLEASE JUST HELP ME.

Answers

Answer:

Umm the pic is blocked

Its the blocked picture or meh

Step-by-step explanation:

Choose 3 values that would make this inequality true: 8 + y ≥ 11

ps help lol

Answers

Numbers 3,4,5 make this inequality true

8+3=11

8+4=12

8+5=13

are 4x and 15 + x equivalent expressions? Explain your reasoning

Answers

Answer:

no.

Step-by-step explanation:

4x means 4 times any given number

15 + x means take any number and add 15.

if x = 2, 4x = 8

if x = 2, 15 + x = 17

i need help with everything please if you help you are a legend

Answers

Answer:

you got this

Step-by-step explanation:

go with your gut and you sure can win

Answer:

I can help.

Step-by-step explanation:

3a is closer to 1, because 12/12 is 1. and 6/12 is 1/2

3b is closer to 0, because 0/6 is o. and 3/6 is 1/2.

3c is 1 and 1 1/12

11/12 + 1/6

find the common denominator. 12. 6×2 and 1×2 then add straight across.

Mrs. Bentiez earns $3,400 every month. She spends 25% of her earnings on rent and saves 12% on food, she saves the rest of her money. How much does Mrs. Bentiez save each month?

Answers

Answer:

$2244

Step-by-step explanation:

Which of the lines below has a negative slope?
A
B
6
-5
15
6
10
5
D
5
5

Answers

Well, negative slope has the word negative in it right? So, it will be the negative number. Answer: -5 (negative 5)

(1 p 18. Demarcus drew a pair of complementary angles. He drew one angle that had a measure of 48º. What was the measure of the other angle he drew? 42° 48° O 132° O 138°​

Answers

Answer: 42

Step-by-step explanation:

Complementary angles are angles in which the sums equal 90.

90 - 48 = 42.

Factor the following polynomials: a^2+a+72

Answers

Answer:

72 + a (1 + a)

Step-by-step explanation:

Which repeated series equals 8×10⁴

8×10×4

8×10+10+10+10


8×10×10×10×10


8×4×4×4×4×4×4×4×4×4×4




Answers

Answer: 8×10×10×10×10

Step-by-step explanation: Hope this helps :)

Answer:

8×10×10×10×10

Step-by-step explanation:

this one

Have a nice day and I hope I helped you:)

Which ratio is equivalent to 17:1?
Ο Α.
A. 17
17
0 B. 34 to 2
O C. 1 through 17
D. 1 to 1

Answers

34:2 or 34 to 2
Hope this helps!❣️

The Difference of 4 and k, divided by 16.

Answers

Answer:4-k÷6

Step-by-step explanation:

please help!
Which transformation could NOT be used to prove that two circles are congruent to one another?

a dilation with a scale factor of 2

a dilation with a scale factor of 1

a reflection

a rotation

Answers

A transformation which can not be used to prove that two circles are congruent to one another is: A. a dilation with a scale factor of 2.

The types of transformation.

In Mathematics, there are different types of transformation and these include the following:

ReflectionRotationTranslationDilation

What is dilation?

Dilation can be defined as a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

In this context, we can reasonably infer and logically deduce that a dilation with a scale factor of 2 would change the size of the two circle and as such making them incongruent.

In conclusion, a dilation with a scale factor of 1, reflection and rotation can be used to congruency in two circles.

Read more on dilation here: brainly.com/question/20482938

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How do I find the x? Please and thank you!

Answers

Answer:

x = 9

Step-by-step explanation:

The two opposite interior angles that are opposite to the exterior angle are congruent as shown in the diagram.

Therefore, based on the exterior angle theorem of a triangle, we have the following equation:

2(7x + 2)° = (17x - 23)

14x + 4 = 17x - 23

Collect like terms

14x - 17x = -4 - 23

-3x = -27

Divide both sides by -3

-3x/-3 = -27/-3

x = 9

Aaron rolls a die 40 times. On 25 of those rolls, he has a 3. Michelle rolls a die 80 times. On 40 of those rolls, she has a 6. Which
statement is TRUE about the experimental and theoretical probabilities?
A)The theoretical probability for rolling a 3 is the same as for rolling a 6.
B)The theoretical probability for rolling a 3 is greater than for rolling a 6.
C)The experimental probability for Aaron's tries is the same as Michelle's
tries.
D)The experimental probability for Aaron's tries is less than the experimental
probability for Michelle's tries.

Answers

Answer:

Pretty sure its D lemme know if I'm right

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