a science experiment begins with a bacterial population of 12. after 1 hour, the population is 18. after 2…

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?

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?

Answer

Answer:

  1. Relationship: Exponential
  2. y - intercept: 12
  3. Rate of change: 1.5

Explanation:

Step1: Identify relationship type

Initial population $P_0 = 12$, at $t = 1$, $P_1=18$, at $t = 2$, $P_2 = 27$. Since $\frac{18}{12}=1.5$ and $\frac{27}{18}=1.5$, it's exponential as ratio of consecutive populations is constant.

Step2: Find y - intercept

The y - intercept is the population at time $t = 0$. Given initial population is 12, so y - intercept is 12.

Step3: Calculate rate of change

The rate of change is the common ratio of consecutive population values. $\frac{18}{12}=\frac{27}{18}=1.5$.