A satellite has a radioisotope power supply. The power output in watts is given by the equation

where t is the time in days and e is the base of natural logarithms.

**a. **How much power will be available at the end of one year?

**Solution: **Applying the given equation, we have

Thus approximately 11.6 watts will be available at the end of one year.

**b. **What is the half-life of the power supply? In other words, how long will it take for the power to drop to half its original strength?

Thus the half-life of the power supply is approximately 173 days. (Note that In x is a shorter expression for log[base e] x.)

**c. **The equipment aboard the satellite requires 10 watts of power to operate properly. What is the operational life of the satellite?

**Solution: **Solving the equation

Hence the operational life of the satellite is 402 days.