The population of lemmings L(t) at the top of a cliff is increasing with the given formula. However, lemmings leap off the cliff at a rate equal to 0.1 L and pile up at the bottom.
a. Write a pure-time differential equation for the number of lemmings B(t) piled up at the bottom of the cliff.
b. Solve using the initial condition B(0) = 0.
c. Graph the number of lemmings at the top and the number at the bottom of the cliff.
d. Find the limit of the ratio B(t)/L(t) = at t approaches infinity.
L(t) = 100 + 100e0.5t.