Question

a biologist is studying the growth of a population of bacteria over time. after collecting data, the biologist performs an exponential regression analysis and obtains the equation ( p = 1000(1.2)^t ), where ( p ) represents the population of bacteria after ( t ) hours. if the biologist started looking at the data at noon, how many bacteria will there be at 3pm? bacteria at 3pm

Explanation:

Step1: Determine the value of \( t \)

From noon to 3 PM, the time elapsed is \( t = 3 \) hours.

Step2: Substitute \( t = 3 \) into the formula \( P = 1000(1.2)^{t} \)

Substitute \( t = 3 \) into \( P=1000(1.2)^{t} \), we get \( P = 1000\times(1.2)^{3} \).
First calculate \( (1.2)^{3}=1.2\times1.2\times1.2 = 1.728 \).
Then \( P=1000\times1.728 \).

Step3: Calculate the value of \( P \)

\( P = 1000\times1.728=1728 \).

Answer:

\( 1728 \)