The formula for the value of a car, C, after t years of depreciation of its initial value v at a rate of r is C=v(1−r)t.

Question

A: How can you rewrite the formula to correctly isolate v?

B: What was the initial value of the car (to the nearest dollar) if it depreciated 10% each year for 10 consecutive years and has a current value of $8,019.60? Select one answer for question A, and one answer for question B. Below are your answers

B: $2,796
A: (1−r)t=v
B: $27,963
B: $23,000
A: C+(1−r)t=v
B: $80,199
B: $8,020
B: $8,019
B: $80,193
A: c(1−r)t=v
A: −(1−r)t=v

So I tried to do this 2 times but I got 2 complete different answers. I don't know what step I'm doing wrong.

The First time I got
A: (1−r)t=v
B: $8,019

Second time I got
c(1−r)t=v
B:$2,796

I tried different formulas because I did not know the format I need to use, Can someone please help me?

Answer 1

You forgot the exponent
C=v (1−r)^t
where v is initial value and C is value after t years
so
v = C / (1-r)^t = C (1-r)^-t

v = 8019.60 / (0.90)^10
= 8019.60 / 0.34868
= 22,999.88 or about 23 thousand

Answer 2

Oh no, wow thank you so much Mr. Damon! I failed the test haha but this will definitely help in the future to make sure to watch my steps!