Answer :
Answer:
14.3
Step-by-step explanation:
A=Pe^{rt}
A=Pe
rt
A=159600\hspace{35px}P=63000\hspace{35px}r=0.065
A=159600P=63000r=0.065
Given values
159600=
159600=
\,\,63000e^{0.065t}
63000e
0.065t
Plug in
\frac{159600}{63000}=
63000
159600
=
\,\,\frac{63000e^{0.065t}}{63000}
63000
63000e
0.065t
Divide by 63000
2.5333333=
2.5333333=
\,\,e^{0.065t}
e
0.065t
\ln\left(2.5333333\right)=
ln(2.5333333)=
\,\,\ln\left(e^{0.065t}\right)
ln(e
0.065t
)
Take the natural log of both sides
\ln\left(2.5333333\right)=
ln(2.5333333)=
\,\,0.065t
0.065t
ln cancels the e
\frac{\ln\left(2.5333333\right)}{0.065}=
0.065
ln(2.5333333)
=
\,\,\frac{0.065t}{0.065}
0.065
0.065t
Divide by 0.065
14.3005532=
14.3005532=
\,\,t
t
t\approx
t≈
\,\,14.3
14.3