Question

a science experiment begins with a bacterial population of 12. after 1 hour, the population is 18. after 2 hours, the population is 27. which best describes the relationship between the time, in hours, and the population of the bacteria? what is the y - intercept of the function? what is the rate of change of the function? add 15 add 6 multiply 15 multiply 6

Explanation:

Step1: Determine the relationship type

We have initial population $P_0 = 12$, after 1 hour $P_1=18$, after 2 hours $P_2 = 27$. Since $\frac{18}{12}=\frac{3}{2}$ and $\frac{27}{18}=\frac{3}{2}$, it is an exponential - growth relationship.

Step2: Find the y - intercept

The y - intercept of a function representing the population over time is the initial population. When time $t = 0$, the population is 12. So the y - intercept is 12.

Step3: Find the rate of change

The rate of change for an exponential function is the common ratio between consecutive terms. $\frac{18}{12}=\frac{3}{2}=1.5$, so we multiply by 1.5 each time.

Answer:

What best describes the relationship between the time, in hours, and the population of the bacteria? Exponential - growth
What is the y - intercept of the function? 12
What is the rate of change of the function? multiply 1.5