Solve the problem.
-A loan of $\$ 8000$ is made at $5 \%$ interest, compounded annually. After t years, the amount due, $A$, is given by the function $\mathrm { A } ( \mathrm { t } ) = 8000 ( 1.05 ) ^ { \mathrm { t } } \text {. }$ Find the doubling time. Round your answer to the nearest tenth.
A) $28.4 \mathrm { yr }$
B) $22.5 \mathrm { yr }$
C) $14.2 \mathrm { yr }$
D) $41.0 \mathrm { yr }$

Question

Quizplus · Accepted Answer

We want to find when the amount due will double, so we want to find when $\mathrm { A } ( \mathrm { t } ) = 2\cdot8000 = 16000$. 
$$16000 = 8000(1.05)^{t}$$
$$2=(1.05)^{t}$$
$$\log_{1.05}(2)=t\approx 14.2$$
So the doubling time is about 14.2 years, which is closest to choice C.

Solve the Problem $8000\$ 8000$8000 Is Made At 5%5 \%5% Interest, Compounded Annually

Solve the Problem $\$ 8000$ Is Made At $5 \%$ Interest, Compounded Annually