Question

4. Imagine the human population of the Earth as an investment that is deposited on the planet with a growth rate-"investment return" of 2% per year, con- tinuously compounded. (The actual current figure is a little lower; if you are curious, look up the latest figure and modify this problem accordingly.) Think of the current population, 7 billion people, as the present value of an invest- ment. Imagine "paying out" a stream of human population, by putting people on spaceships to leave the planet. Suppose the exodus happens at a constant rate of R humans per year, forever. Use the present value formula to calculate the rate R. (In population biology, R is called the harvest rate.

Answer 1

0=+7-R*e^(-0.02*1)-R*e^(-0.02*2)......

0=7-R*e^(-0.02*1)/(1-e^(-0.02))

=>R=7*e^(0.02*1)*(1-e^(-0.02))

=>R=0.1414 billion