Respuesta :
Answer:
A=Pe^{rt}
A=Pe
rt
A=152800\hspace{35px}P=79000\hspace{35px}r=0.068
A=152800P=79000r=0.068
Given values
152800=
152800=
\,\,79000e^{0.068t}
79000e
0.068t
Plug in
\frac{152800}{79000}=
79000
152800
=
\,\,\frac{79000e^{0.068t}}{79000}
79000
79000e
0.068t
Divide by 79000
1.9341772=
1.9341772=
\,\,e^{0.068t}
e
0.068t
\ln\left(1.9341772\right)=
ln(1.9341772)=
\,\,\ln\left(e^{0.068t}\right)
ln(e
0.068t
)
Take the natural log of both sides
\ln\left(1.9341772\right)=
ln(1.9341772)=
\,\,0.068t
0.068t
ln cancels the e
\frac{\ln\left(1.9341772\right)}{0.068}=
0.068
ln(1.9341772)
=
\,\,\frac{0.068t}{0.068}
0.068
0.068t
Divide by 0.068
9.7012062=
9.7012062=
\,\,t
t
t\approx
t≈
\,\,10
10
Round to the nearest year
Your Solution:
10
Step-by-step explanation:
