Chapter 7, Problem 57SGR

To determine

The number of bacteria in the dish at 5:00 P.M.

Answer to Problem 57SGR

The estimated number of bacteria is 567.8.

Explanation of Solution

Given information: The equation given $p=550{(2.7)}^{0.008t}$ , where p is the population of bacteria and t is the number of hours and t=0 corresponds at 1:00 P.M.

Calculation:

Given t=0 is at 1:00 P.M.

So at 5:00 P.M, the number of hours $t=(5:00-1:00)=4$ hours.

Now by using the given equation,

  $\begin{array}{l}$ p=550{(2.7)}^{0.008t}$$ \Rightarrow p=550{(2.7)}^{0.008\times 4}$$ \Rightarrow p=550{(2.7)}^{0.032}$\Rightarrow p=550(\text{1}\text{.0322945641774092})\\ \Rightarrow p=\text{567}\text{.7620}\\ \Rightarrow p=567.8\end{array}$

So, the estimated number of bacteria in the dish at 5:00 P.M is 567.8 [ to the nearest tenth].