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A car was valued at $38,000 in the year 1994. The value depreciated to $14,000 by the year 2004.

A) What was the annual rate of change between 1994 and 2004?
r =
Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r= %.
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2007 ?
value = $
Round to the nearest 50 dollars.

1 Answer

4 votes
A) To find the annual rate of change, we can use the formula:

r = (V2/V1)^(1/n) - 1

where V1 is the initial value, V2 is the final value, n is the number of years, and r is the annual rate of change (expressed as a decimal).

Plugging in the given values, we get:

r = (14000/38000)^(1/10) - 1

r ≈ -0.1102

So the annual rate of change between 1994 and 2004 is approximately -0.1102.

B) To convert the rate to a percentage, we can multiply by 100:

r ≈ -11.02%

So the correct answer to part A written in percentage form is approximately -11.02%.

C) To find the value of the car in 2007, we can use the formula:

V = V0*(1+r)^n

where V0 is the initial value, r is the annual rate of change (expressed as a decimal), n is the number of years, and V is the final value.

We want to find the value in 2007, which is 3 years after 2004. So we plug in:

V0 = 14000 (since that was the value in 2004)
r = -0.1102 (the annual rate of change)
n = 3 (the number of years since 2004)

V = 14000*(1-0.1102)^3

V ≈ $9,679.65

Rounding to the nearest 50 dollars, we get:

value ≈ $9,700

Therefore, the value of the car in the year 2007 is approximately $9,700.
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