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sweet-ann [11.9K]
2 years ago
6

Jack invested some money in a bank at a fixed rate of interest compounded annually. The equation below shows the value of his in

vestment after x years:
f(x) = 300(1.02)x

What was the average rate of change of the value of Jack's investment from the third year to the fifth year?
Mathematics
2 answers:
postnew [5]2 years ago
5 0
Jack's investment on the third year
f(3) = 300(1.02)³ = 318.36 (rounded to 2 decimal place)

Jack's investment on the fifth year
f(5) = 300(1.02)⁵ = 331.22 (rounded to 2 decimal place)

The average rate of change from year 3 to year 5  = (331.22 - 318.36) ÷ (5 - 3)
The average rate of change = 12.86 ÷ 2 = 6.43
masya89 [10]2 years ago
5 0
The equation is f(x) = 300 * (1.02)^x

1) Evaluate the equation for x = 3 years and x = 5 years

x = 3 => f(3) = 300 * (1.02)^3 = $318.3624

x= 5 => f(5) = 300 * (1.02)^5 = $331.2242

2) The average rate of change is [change in f(x) ] / [change in x]

change in f(x) = f(5) - f(3) = $12.8678

change in x = 5year - 3 year = 2 year

Average rate of change = $12.8678 / 2 year = $6.43 / year   <---- answer

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The reciprocal parent function would be, F(x)= 1/x
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2 years ago
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If $10,000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of in
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Answer: C. 10000n\dfrac{x}{100}

Step-by-step explanation:

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Time period :  n years

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S.I.=\dfrac{P\times R\times T}{100}

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it can also be written as \Rightarrow\ S.I.=10000n\dfrac{x}{100}

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2 years ago
Merle Fonda opened a new savings account. She deposited $40,000 at 10% compounded semiannually. At the start of the fourth year,
IrinaVladis [17]
Use compound interest formula  F=P(1+i)^n twice, one for each deposit and sum the two results.

For the P=$40,000 deposit,
i=10%/2=5%  (semi-annual)
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For the P=20000, deposited at the START of the fourth year, which is the same as the end of the third year.
i=5% (semi-annual
n=2*(6-3), n = 6 
Future value (at end of year 6)
F=P(1+i)^n = 20000(1+0.05)^6 = 26801.913

Total amount after 6 years
= 71834.253 + 26801.913
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8 0
1 year ago
Find the area of the shape shown below.
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31.5

Step-by-step explanation:

We can add the areas together

We have a rectangle and a triangle

The area of the rectangle is

A = lw

   = 7*3

   = 21

The area of the triangle is

A = 1/2 bh

   = 1/2 (7)*3

   = 21/2

   = 10.5

Add them together

A = 21 + 10.5

   =31.5

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The first equation in the system models the heights in feet, h, of a falling baseball as a function of time, tThe second equatio
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The height of the baseball is 35 feet at the moment the player begins to leap.

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