Question

1. the amount of bacteria in a petri dish doubles every 3 hours starting with 100 cells and can be represented with the function ( p(t)=100(2)^{t} ).

a. how many hours have passed in the expression ( 100(2)^{8} )?
b. write an expression that represents how much the population has grown in 1 day.

Explanation:

Step1: Analyze the exponent for part a

The function is \(p(t)=100(2)^{t}\), where \(t\) represents the number of 3 - hour intervals. In the expression \(100(2)^{8}\), the exponent \(t = 8\). Since each \(t\) corresponds to 3 hours, the number of hours passed is \(3\times t\).

$$3\times8=24$$

Step2: Determine the number of 3 - hour intervals in a day for part b

There are 24 hours in a day. Since each interval is 3 hours, the number of intervals \(t=\frac{24}{3}=8\). The population function is \(p(t)=100(2)^{t}\), so for \(t = 8\), the expression is \(100(2)^{8}\)

Answer:

a. 24 hours
b. \(100(2)^{8}\)