Chapter 7.1, Problem 7STP

The number of bacteria in a culture quadruples every hour. There were 65,536 bacteria in the culture at 8: 00 A.M. The expression $65,536\cdot 4^h$ models the number of bacteria in the culture $h$ hours after 8: 00 A.M.

a. What is the value of the expression for $h=-4?$

b. What does the value of the expression in part a represent?

To determine

To determine the value of a given expression at a given value and state its significance.

Answer to Problem 7STP

1024 ; it is the number of bacteria present at 4:00 AM

Explanation of Solution

Given: Number of bacteria at 8:00 AM is given which is 65536. The expression to model number of bacteria present h hours after 8:00 PM is given. The expression is $65536·4^h$ . Value of this expression is to be calculated at h = (-4) and its significance is to be determined.

Calculation:

At h = -4

  $\begin{array}{l}=65536·4^{-4}\\ =65536·\frac{1}{4^4}\\ =\frac{65536}{4^4}\\ =\frac{65536}{64}\\ =1024\end{array}$

It represents the number of bacteria 4 hours before 8:00 AM. It means, it represents the number of bacteria present at 4:00 AM.