A) To find the annual rate of change, we can use the formula:
r = (V2/V1)^(1/n) - 1
where:
V1 = initial value ($42,000)
V2 = final value ($11,000)
n = number of years (2006 - 1994 = 12)
Plugging in the values, we get:
r = (11000/42000)^(1/12) - 1 ≈ -0.1135
Therefore, the annual rate of change between 1994 and 2006 is approximately -0.1135.
B) To convert the rate of change to a percentage, we can multiply by 100 and add a percent sign:
r = -0.1135 × 100% ≈ -11.35%
Therefore, the correct answer to part A written in percentage form is approximately -11.35%.
C) Assuming the car value continues to drop by the same percentage, we can use the formula for exponential decay:
V = V0 * (1 - r)^t
where:
V0 = initial value ($11,000 in 2006)
r = annual rate of change (-0.1135)
t = number of years (2010 - 2006 = 4)
Plugging in the values, we get:
V = 11000 * (1 - (-0.1135))^4 ≈ $6,250
Therefore, the value of the car in the year 2010 would be approximately $6,250, rounded to the nearest 50 dollars.