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.