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.