A population of algae in a pond grows exponentially at a rate of for the first 2 hours

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A population of algae in a pond grows exponentially at a rate of

0.40\,\text{h}^{-1}

for the first 2 hours. After nutrients diminish, the growth rate drops to

0.10\,\text{h}^{-1}

and remains constant thereafter. If the initial population is 100 cells, calculate the population after 5 hours.