Chapter 5.5, Problem 77E

(a)

To determine

To find: The increase in the population of a culture of bacteria with $r=2$ over the time interval $0\le t\le 4$ using the population growth rate model $p^{\prime }\left(t\right)=\frac{200}{{\left(t+1\right)}^r}$ bacteria per hour, for $t\ge 0$ and $r>1$.

(b)

To determine

To find: The increase in the population of a culture of bacteria with $r=2$ over the time interval $0\le t\le 4$ using the population growth rate model $p^{\prime }\left(t\right)=\frac{200}{{\left(t+1\right)}^r}$ bacteria per hour, for $t\ge 0$ and $r>1$.

(c)

To determine

To explain: The increase in population $\Delta P$ is increase or decrease with parameter $r$ overt the time interval $\left[0,T\right]$ for fixed $T$.

(d)

To determine

To estimate: The value of $r$ that gives the best fit of the data measures by a lab technician of an increase in the population of 350 bacteria over the 10-hr period $\left[0,10\right]$.

(e)

To determine

To find: The increases in the population over the time interval $\left[0,T\right]$ any for $T>0$, by using the population model in part (b) does the bacteria population increases without bound or does it approach a finite limit as $T\to \infty$.