Chapter 12.5, Problem 61E

(a)

To determine

To find: The expression for $N\left(t\right)$ by using the properties of logarithms and $N_0=1000$.

(b)

To determine

To estimate: The derivative of $N\left(t\right)$ when $t=20$ using the graphing calculator and to interpret the answer.

(c)

To determine

To sketch: The graph of $S\left(t\right)$ on $\left[0,35\right]$ by $\left[0,12\right]$ using the graphing calculator.

(d)

To determine

To sketch: The graph of $N\left(t\right)$ on $\left[0,35\right]$ by $\left[0,20000000\right]$ using the graphing calculator and to compare the graphs from part (c) and part (d).

(e)

To determine

To find: The value of $\underset{t\to \infty }{\lim }S\left(t\right)$ and to estimate the $\underset{t\to \infty }{\lim }N\left(t\right)$.