Question

a population of bacteria is growing in a petri dish. the function $a(t) = 10(1.02^t)$ models the population with $a(t)$ representing the number of bacteria at time, $t$, in hours. complete the statements. based on the function, $a(t)$, 10 is the initial number of bacteria in the petri dish. the number of bacteria is dropdown with options: increasing by 2% each hour, decreasing by 98% each hour, increasing by 10% per hour.

Explanation:

Step1: Recall exponential growth form

The standard exponential growth function is $A(t) = A_0(1+r)^t$, where $A_0$ is the initial amount, $r$ is the growth rate per period, and $t$ is time.

Step2: Match given function to standard form

The given function is $A(t)=10(1.02)^t$. Comparing to $A_0(1+r)^t$, we see $1+r=1.02$.

Step3: Calculate growth rate

Solve for $r$: $r=1.02-1=0.02$, which is 2%. This means the population grows by 2% each hour.

Answer:

increasing by 2% each hour