Question

to begin a bacteria study, a petri dish had 1900 bacteria cells. each hour since, the number of cells has increased by 12%. 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 \( a \) and \( r \)

Here, the initial number of bacteria \( a = 1900 \). The growth rate is \( 12\% = 0.12 \), so \( 1 + r = 1 + 0.12 = 1.12 \).

Step3: Substitute into the formula

Substitute \( a = 1900 \) and \( 1 + r = 1.12 \) into the exponential growth formula. We get \( y = 1900(1.12)^t \).

Answer:

\( y = 1900(1.12)^t \)