Chapter 5 - Section 5.4 - Indefinite Integrals and the Net Change Theorem - 5.4 Exercises - Page 411: 71

The bacteria population after one hour is $~5443$

We can find the population $P(1)$ after one hour: $P(1) = 4000+\int_{0}^{1}1000\cdot 2^t~dt$ $P(1) = 4000+1000\cdot (\frac{2^t}{ln~2})\vert_{0}^{1}$ $P(1) = 4000+1000 \cdot (\frac{2^1}{ln~2}-\frac{2^0}{ln~2})$ $P(1) = 4000+1000 \cdot (\frac{2}{ln~2}-\frac{1}{ln~2})$ $P(1) = 4000+1000 \cdot (\frac{1}{ln~2})$ $P(1) = 5443$ The bacteria population after one hour is $~5443$