A car was valued at $40,000 in the year 1990. The value depreciated to $13,000 by the year 2006. What was the annual rate of change between 1990 and 2006

Question

A car was valued at $40,000 in the year 1990. The value depreciated to $13,000 by the year 2006.

A) What was the annual rate of change between 1990 and 2006? (round your answer to 4 decimal places)

B) What is the correct answer to part A written in percentage form?

C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2010 ? (round you answer to the nearest $50)

Answer 1

13000 = 40000 e^16k

0.325 = e^16k

ln 0.325 = 16k

-1.1239 ≈ 16k

Determine k, then the annual rate is e^k