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 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

Substitute $t = 3$ into the equation $P=1000(1.2)^t$. We get $P = 1000\times(1.2)^3$.

Step3: Calculate $(1.2)^3$

$(1.2)^3=1.2\times1.2\times1.2 = 1.728$.

Step4: Calculate P

$P=1000\times1.728 = 1728$.

Answer:

1728