pre calc question

Question

A car was valued at $37,000 in the year 1993. The value depreciated to $15,000 by the year 2003.

A) What was the annual rate of change between 1993 and 2003? 

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.

Answer 1

A) P(t) = 37000(1 + r)^t, where t is number of years since 1993. In 2003 t = 2003 - 1993 = 10 years and P(10) = 15000; 15000 = 37000(1 + r)¹0; so, r = (15/37)^1/10 - 1 = - 0.086331 = - %8.6331

B) In 2007 t = 2007 - 1993 = 14.

So, P(14) = 37000(1 - 0.086331)¹⁴ = $10453.13 = $10450