Answer
(a). $A(t)=5664.978$
(b). $t=8.08$
(c). $t=3.96$
Work Step by Step
The formula for periodically compounded interest rate is, $A(t)=P(1+\frac{r}{n})^{nt}$. Whereas, $P$ is the Initial investment, $r$ is the rate, $n$ is a number of times it is compounded.
Meanwhile, The formula for continuously compounded interest rate is, $A(t)=Pe^{rt}$.
$P=5000$, $r=0.085$, $n=2$
(a). $t=1.5$
$A(t)=5000(1+\frac{0.085}{2})^{2\times1.5}=5664.978$
(b).$7000=5000(1+\frac{0.085}{2})^{2t},$
$1.4=(1.0425)^t,$
$\log 1.4=t\log 1.0425$
$t=8.08$
(c). $A(t)=Pe^{rt}$.
$7000=5000e^{0.085t},$.
$1.4=e^{0.085t},$.
$\ln 1.4=0.085t,$
$t=3.96$
