Question

A painting is purchased as an investment for $125. If its value increases continuously so that it doubles every 3years, then its value is given by the functionV(t) = 125-2/3 for t≥ 0where t is the number of years since the painting was purchased, and V(t) is its value (in dollars) at time t. FindV(9) and V(12).V(9) = $V(12) = $

Answer 1

Given:

$V(t)=125\cdot2^{\frac{t}{3}}$

Find: (a) V(9)

(b)V(12)

Explanation: (a)

$\begin{gathered} V(t)=125\cdot2^{\frac{t}{3}} \\ V(9)=125\cdot2^{\frac{9}{3}} \\ =125\cdot2^3 \\ =125\cdot8 \\ =1000\text{ \ } \end{gathered}$

(b)

$\begin{gathered} V(t)=125\cdot2^{\frac{t}{3}} \\ V(12)=125\cdot2^{\frac{12}{3}} \\ =125\cdot2^4 \\ =125\cdot16 \\ =2000\text{ \ } \end{gathered}$