Answer: A.
[tex]\frac{\operatorname{\ln}(1.22)}{5}[/tex]
Explanation
We are given the equation:
[tex]A(t)=3,531\cdot e^{(rt)}[/tex]
As we are said that the account balance is $4,313 after 5 years, then we can replace the values as follows:
[tex]4,313=3,531e^{(r\cdot5)}[/tex]
Thus, we have to isolate for r:
[tex]\frac{4,313}{3,531}=\frac{3,531e^{(r\times5)}}{3,531}[/tex][tex]1.22=e^{5r}[/tex]
Then, we apply a natural logarithm to both sides of the equation to cancel out the Euler constant.
[tex]\ln(1.22)=\ln(e^{5r})[/tex][tex]\operatorname{\ln}(1.22)=5r[/tex]
Finally, we divide both sides of the equation against 5:
[tex]r=\frac{\ln(1.22)}{5}[/tex]
