1. The population of bacteria after time t, is given by the formula:
P(t)=[tex]I e^{kt} [/tex],
where I is the initial population and k the growth constant.
For example, the population at time t=0 is P(0)=[tex]I e^{k0}=Ie^{0}=I*1=I[/tex]
2.
P(t)=[tex]2000 e^{kt} [/tex]
we can use the information we have:
P(4)=2,600= [tex]2000 e^{4k}[/tex]
[tex] ( e^{k} )^{4}= \frac{2,600}{2000} [/tex]
[tex]( e^{k} )^{4}= 1.3[/tex]
[tex]e^{k}= \sqrt[4]{1.3} = \sqrt[2]{ \sqrt[2]{1.3} }= \sqrt[2]{1.14} =1.068[/tex]
3.
So the function becomes P(t)=[tex]2000 e^{kt}=2000 ( e^{k}) {t} =2000 (1.068)^{t} [/tex]
4. Population after 17 hours is P(17)=[tex]2000(1.068)^{17}=2000*3.06=[/tex] 6120
