Answer
a) The growth rate is $10^4$ bacteria/hr.
b) The growth rate is $0$ bacteria/hr.
c) The growth rate is $-10^4$ bacteria/hr.
Work Step by Step
$$b=10^6+10^4t-10^3t^2$$
The growth rate at time $t$ is the derivative of the size of the population at time $t$, for which reason we will call this growth rate $b'(t)$:
$$b'(t)=10^4-2\times10^3t$$
a) At $t=0$ hours: $$b'(0)=10^4-2\times10^3\times0=10^4(bacteria/hr)$$
b) At $t=5$ hours: $$b'(5)=10^4-2\times10^3\times5=10^4-10^4=0(bacteria/hr)$$
a) At $t=10$ hours: $$b'(10)=10^4-2\times10^3\times10=10^4-2\times10^4=-10^4(bacteria/hr)$$
