Another bacteria growth problem

[karush]

$\tiny{205.22}$
$$\displaystyle
b'(t)=8^5-2(8^4)(t) \\
b'(0)=8^5-2(8^4)(0)=8^5=3.3 \cdot 10^4 \, \frac{p}{h} \\
b'(4)=8^5-2(8^4)(4)=0 \,\frac{p}{h} \\
b'(8)=8^5-2(8^4)(8)=-8^5=-3.3 \cdot 10^4 \, \frac{p}{h}$$
$$\text{suggestions?}$$

 

[Greg]

What is $p$? What is $h$?

 

[Monoxdifly]

My guess is he denoted "population" as p and "hours" as h.

 

[karush]

yep

 

[HallsofIvy]

"population" is not a unit of quantity! It looks to me like the formula, which says "b= " gives the number of bacteria so a better quantity would be "bacteria per hour". In any case, I don't see any reason for the "3.3". Were you told to "round off" and give an approximate answer? The formula given is $$b= 8^6+ 8^5 t+ 8^4t^2$$. The rate of growth is given by $$b'= 8^5+ 2(8^4)t$$.

When t= 0, that is $$b'= 8^5$$. When t= 4, that is $$b'= 8^5+ 2(8^4)(4)= 8^5+ 8(8^4)= 2(8^5)$$. When t= 8, that is $$b'= 8^5+ 2(8^4)(8)= 8^5+ 2(8^5)= 3(8^5)$$.