Question

at noon, to begin a study, a petri dish had 3000 bacteria cells. each hour since, the number of cells has increased by 11%. let t be the number of hours since the start of the study. let y be the number of bacteria cells. write an exponential function showing the relationship between y and t.

Explanation:

Step1: Recall Exponential Growth Formula

The general form of an exponential growth function is \( y = a(1 + r)^t \), where \( a \) is the initial amount, \( r \) is the growth rate (in decimal), and \( t \) is time.

Step2: Identify Values of \( a \) and \( r \)

Here, the initial number of bacteria \( a = 3000 \). The growth rate is \( 11\% = 0.11 \), so \( 1 + r = 1 + 0.11 = 1.11 \).

Step3: Substitute into Formula

Substitute \( a = 3000 \) and \( 1 + r = 1.11 \) into the exponential growth formula. We get \( y = 3000(1.11)^t \).

Answer:

\( y = 3000(1.11)^t \)