## Calculus 8th Edition

$11, 713$ bacteria
A bacteria population starts with 400 bacteria and grows at a rate of $r(t)=450.268 e^{1.12567t}$ bacteria per hour. Calculate the bacteria rate after three hours. Consider $r'(t)$ amount of the bacteria rate after three hours if we starts the bacteria population with 400 bacteria. Then $r'(3)=400+\int _{0}^{3}r(t)dt$ This implies $r'(3)=400+\int _{0}^{3} 450.268( e^{1.12567t}) dt$ $=400+450.268(\frac{e^{1.12567t}}{1.12567})_{0}^{60}$ $=400+\frac{450.268}{1.12567}({e^{1.12567\times 3}-1})$ $\approx 11, 713$ bacteria Hence, the amount of the bacteria rate after three hours will be $11, 713$ bacteria .