Chapter 8.8, Problem 16HP

To determine

To explain: The equation approaches but never reaches c.

Answer to Problem 16HP

The expiation is shown above.

Explanation of Solution

Given information:

The given equation is $f(t)=\frac{c}{1+60e^{-0.5t}}$

Calculation:

Consider the function ,

  $f(t)=\frac{c}{1+60e^{-0.5t}}$

This is because , the denominator is an exponential decay function and as $t$ goes to positive infinity the expression $e^{-0.5t}$ approaches $0$ but can never be equal to $0$ . That is why the function never reaches $c$ .

Hence proved.