Answer
a) $10^{4}\,bacteria/h $
b) $0\,bacteria/h $
c) $-10^{4}\,bacteria/h $
Work Step by Step
The growth rate is given by:
$ b'(t)=\frac{d}{dt}(10^{6}+10^{4}t-10^{3}t^{2})=10^{4}-2\times10^{3}\times t=10^{4}-2000t $
a) When $ t=0\,h $, the growth rate= $ b'(0)=10^{4}-2000(0)=10^{4}\,bacteria/h $
b) When $ t=5\,h $, the growth rate= $ b'(5)=10^{4}-2000(5)=0\,bacteria/h $
c) When $ t=10\,h $, the growth rate= $ b'(10)=10^{4}-2000(10)=-10^{4}\,bacteria/h $
