A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 7(1.06)
Part A: When the biologist concluded her study, the radius of the algae was approximately 13.29 mm. What is a reasonable domain to plot the growth
function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 4 to d = 11, and what does it represent? (4 points)

A) The reasonalbe domain to plot the graph is 0 ≤ d ≤ 11 (days)

B) The y-intercept of the graph of the function f(d) represents the radius of the algae when the biologist started her study

C) The average rate from d = 4 to d = 11 is:

       

It represents that the radius of the algae increased an average of 0.6358mm per day from the fourth day until the last day of her study.

Explanation:

Start writting the equation properly

       

Where f(d) is in mm, and d is number of days.

Part A: When the biologist concluded her study, the radius of the algae was approximately 13.29 mm. What is a reasonable domain to plot the growth function?

The domain should be the whole numbers since the moment the study starts (d = 0) up to the moment the biologist concluded her study.

To determine the number of days elapsed, you solve the equation for d and find it when f(d) is 13.29mm

           

Therefore, the domain is 0 ≤ d ≤ 11 (days)

Part B: What does the y-intercept of the graph of the function f(d) represent?

The y-intercept of a function is the value of the function for which its graph intercepts the vertical axis.

That happens when the independent variable, d in this case, is equal to zero: f(0).

d = 0 represents the moment when the biologist started her study, meaning that f(0) is the radius of the algae when the study started

To find the y-intercept you make d = 0 in the equation and fin find f(0)

That is:

       

Then, the y-intercept, the radius of the algae when the biologist started her study, is 7 mm.

Part C: What is the average rate of change of the function f(d) from d = 4 to d = 11, and what does it represent?

The average rate of change of the function f(d) from d = 4 to d = 11 is:

     

     

       

That means that the radius of the algae increased an average of 0.6358mm per day from the fourth day until the last day of the study.