Question

modeling a problem situation with a 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?
exponential
what is the y - intercept of the function?
12
what is the rate of change of the function?
add 1.5
add 6
multiply 1.5
multiply 6

Explanation:

Step1: Recall exponential - function form

The general form of an exponential function is $y = ab^{x}$, where $a$ is the y - intercept and $b$ is the base. The y - intercept is the value of $y$ when $x = 0$. Given that the initial population (when $x = 0$) is 12, so the y - intercept is 12.

Step2: Calculate the rate of change

We know that at $x = 0$, $y=12$, and at $x = 1$, $y = 18$. To find the rate of change in an exponential function, we use the formula $\frac{y_1}{y_0}$. Here, $y_0 = 12$ (when $x = 0$) and $y_1=18$ (when $x = 1$). So the rate of change $b=\frac{18}{12}=1.5$, which means we multiply by 1.5 each time.

Answer:

The rate of change of the function is multiply 1.5.