Answer:
A. [tex]t=25\ln(5)[/tex]
Step-by-step explanation:
We want to solve for t in [tex]500=100e^{0.04t}[/tex]
Divide through by 100
[tex]5=e^{0.04t}[/tex]
Take natural logarithm of both sides
[tex]\ln(5)=\ln(e^{0.04t})[/tex]
This simplifies to: [tex]\ln(5)=0.04t[/tex]
Divide both sides by 0.04
[tex]\frac{\ln(5)}{0.04}=t[/tex]
[tex]t=25\ln(5)[/tex]
