Chapter 4.5, Problem 60E

To determine

(a)

To find:

An expression for $N\left(t\right)$. Assume that $N_0=1000$ and $\ln \left(\frac{N\left(t\right)}{N_0}\right)=9.8901e^{-e^{2.54197-0.2167t}}$

To determine

(b)

To estimate:

The derivative of $N\left(t\right)=1000e^{\left(9.8901e^{-e^{2.54197-0.2167t}}\right)}$ when $t=20$ using the graphing calculator.

To determine

(c)

To sketch:

The graph of the function $S\left(t\right)$ on $\left[0,35\right]$ by $\left[0,12\right]$, let $S\left(t\right)=\ln \left(\frac{N\left(t\right)}{N_0}\right)$

To determine

(d)

To sketch:

The graph of the function $N\left(t\right)$ on $\left[0,35\right]$ by $\left[0,\mathrm{20,\; 000,\; 000}\right]$

To determine

(e)

To find:

$\underset{t\to \infty }{\lim }S\left(t\right)$ and then use this limit to find $\underset{t\to \infty }{\lim }N\left(t\right)$