Answer
a) After almost 2 years.
b) After almost 6 and a half years.
c) After a little more than 9 years.
Work Step by Step
a) Replace V(t) with 16,000 and solve for t:
$16,000=18,955(0.905)^{t}$
$\dfrac{16,000}{18,955}=0.905^{t}$
$t=\log_{0.905}\dfrac{16,000}{18,955}$
$t=\dfrac{\log\frac{16,000}{18,955}}{\log0.905}$
$t\approx\dfrac{-0.0736}{-0.0434}$
$t\approx1.7$
b) Replace V(t) with 10,000 and solve for t:
$10,000=18,955(0.905)^{t}$
$\dfrac{10,000}{18,955}=0.905^{t}$
$t=\log_{0.905}\dfrac{10,000}{18,955}$
$t=\dfrac{\log\frac{10,000}{18,955}}{\log0.905}$
$t\approx\dfrac{-0.2777}{-0.0434}$
$t\approx6.4$
c) Replace V(t) with 7500 and solve for t:
$7500=18,955(0.905)^{t}$
$\dfrac{7500}{18,955}=0.905^{t}$
$t=\log_{0.905}\dfrac{7500}{18,955}$
$t=\dfrac{\log\frac{7500}{18,955}}{\log0.905}$
$t\approx\dfrac{-0.4027}{-0.0434}$
$t\approx9.3$