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?

Explanation:

Step1: Determine the value of t

The biologist starts looking at data at noon and we want to find the population at 3 PM. So the time elapsed $t = 3$ hours.

Step2: Substitute t into the formula

We have the formula $P = 1000(1.2)^t$. Substitute $t = 3$ into it, so $P=1000\times(1.2)^3$.

Step3: Calculate the value of P

$(1.2)^3=1.2\times1.2\times1.2 = 1.728$. Then $P = 1000\times1.728=1728$.

Answer:

1728