Question

A painting is purchased for $500. If the value of the painting doubles every 5 years, then its value is given by the function V(t) = 500 • 2t/5, where t is the number of years since it was purchased and V(t) is its value (in dollars) at that time. What is the value of the painting ten years after its purchase?

Answer 1

Your function description suffered a little in the translation. The correct function is\[V(t) = (500) 2^{t/5}\]If you substitute ten in for t, you get\[V(10) = (500) 2^{10/5}=(500)2^2=2000\]You could also figure it out without using the function by noting that in ten years, the value had doubled exactly twice.