Answer:
12.9
Step-by-step explanation:
30400=
30400=
\,\,22000e^{0.025t}
22000e
0.025t
Plug in
\frac{30400}{22000}=
22000
30400
=
\,\,\frac{22000e^{0.025t}}{22000}
22000
22000e
0.025t
Divide by 22000
1.3818182=
1.3818182=
\,\,e^{0.025t}
e
0.025t
\ln\left(1.3818182\right)=
ln(1.3818182)=
\,\,\ln\left(e^{0.025t}\right)
ln(e
0.025t
)
Take the natural log of both sides
\ln\left(1.3818182\right)=
ln(1.3818182)=
\,\,0.025t
0.025t
ln cancels the e
\frac{\ln\left(1.3818182\right)}{0.025}=
0.025
ln(1.3818182)
=
\,\,\frac{0.025t}{0.025}
0.025
0.025t
Divide by 0.025
12.9360062=
12.9360062=t
t = 12.9
12.9
