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.

Answer 1

Let x be the number of years since the purchace
f(x) = (initial value)*(rate of growth)^x
If it is depreciating at a rate of 15% in one year, then the value that remains is 85% of the original value. So the rate should be 0.85. So
f(x) = 1000*(0.85)^x
Just to check:
f(0) = 1000(0.85)^0 = 1000 \(\surd\)
f(1) = 1000(0.85)^1 = 850 \(\surd\)

Answer 2

v(t) = 1000(0.85)t; the value will fall below $100 in about 14.2 yr. ??