Question

a study is done on the number of bacteria cells in a petri dish. suppose that the population size p(t) after t hours is given by the following exponential function. p(t)=2300(0.92)^t find the initial population size. does the function represent growth or decay? growth decay by what percent does the population size change each hour? %

Explanation:

Step1: Find initial population size

The exponential function is in the form \( P(t) = a(b)^t \), where \( a \) is the initial population. Here, \( P(t) = 2300(0.92)^t \), so \( a = 2300 \).

Step2: Determine growth or decay

In \( P(t) = a(b)^t \), if \( 0 < b < 1 \), it's decay. Here, \( b = 0.92 \), so it's decay.

Step3: Find percent change

The formula for percent change is \( (1 - b) \times 100\% \). Substitute \( b = 0.92 \): \( (1 - 0.92) \times 100\% = 0.08 \times 100\% = 8\% \) decay.

Answer:

Initial population size: 2300; Function represents: decay; Percent change: 8%