We are asked to solve the following for t.
First, divide each side by 10.
500=10e^(0.04t) --> 50=e^(0.04t)
Now take the natural logarithm (ln) of each side. We use the ln function instead of the log function due to the presence of the e.
ln50=lne^(0.04t) --> 3.9120=0.04t
We have gotten rid of the exponent, now we can solve for t by dividing both sides by 0.04.
3.9120=0.04t --> 97.8006=t
So the value of t to four decimal places is 97.8006.