Solve for t. 500 = 10e^(.04t) (Instead of a log on each side, do an ln on each side.) Give your answer correct to four decimals. 

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ncchemist eNotes educator| Certified Educator

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.