# 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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Expert Answers

ncchemist | Certified Educator

We are asked to solve the following for t.

500=10e^(0.04t)

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.**