Question

A motor scooter purchased for $1,000 depreciates at an annual rate of 15%. Write an exponential function, and graph the function. Use the graph to predict when the value will fall below $100.

1. v(t) = 0.85(1000)t; the value will fall below $100 in about 18 yr.
2. v(t) = 1000(0.85)t; the value will fall below $100 in about 18 yr.
3. v(t) = 0.85(1000)t; the value will fall below $100 in about 14.2 yr.
4. v(t) = 1000(0.85)t; the value will fall below $100 in about 14.2 yr.

Answer 1

but ecording to the equation the function must be exponential, how come the answer are given as a linear function?

Answer 2

@JamenS

Answer 3

@JamenS i suppose that t is an exponent. so let: v(t)=final prize of the scooter...t=time in years.....p=initial prize of the scooter . r= rate of depreciation per year so v(t)=p(1-r)^t.... does this help?

Answer 4

Do you have a calculator?

Answer 5

it loses 15% of its value, i.e. it retains 85% of its value
use \(V=1000\times (.85)^t\)

Answer 6

solve \(1000\times (.85)^t=100\) in two steps
1) divide both sides by \(1000\) to get \((.85)^t=0.1\)
2) use the change of base formula which says \(b^x=A\iff x=\frac{\ln(A)}{\ln(b)}\)

Answer 7

oh third step is a calculator