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

V(t) = 500 * (2t)/5
after 10 years....t = 10
V(10) = 500 * (2(10))/5 =
             500 * 20/5 =
             10,000/5=
              $ 2000...its worth 2000 bucks

Answer 2

Answer: $2,000

Step-by-step explanation:

Given: The purchasing price of painting = $500

If the value of the painting doubles every 5 years, then its value is given by the function $V(t)=500(2)^{\frac{t}{5}}$, where t is the number of years since it was purchased and V(t) is its value (in dollars) at that time.

The value of the painting ten years after its purchase is given by :-

$V(10)=500(2)^{\frac{10}{5}}\\\\=500(2)^2\\\\=500(4)=2,000$

Hence, the value of the painting ten years after its purchase = $2,000