Question

A car was valued at $38,000 in the year 1993. The value depreciated to $11,000 by the year 2004.

A) What was the annual rate of change between 1993 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

Answer 1

2004 - 1993 = 11 years
11,000 = 38,000 *x^11
x^11 = 11/38 = 0.289473684
11 log x = -0.538390911
log x = -0.048944628
x = .893419385
r = 1-x = 0.106580614 = 0.1066 or down 10.66 % per year
2007 - 1993 = 14 years old
38,000 * .893419385^14 = 7844.28 = $7,850