Question

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) = 9(1.04)d

Part A: When the biologist concluded her study, the radius of the algae was approximately 12.81 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 = 3 to d = 9, and what does it represent? (4 points)

Answer 1

A: The reasonable domain to plot the growth function would be all positive integers for the number of days, d, since the growth occurs over time.

B: The y-intercept of the graph of the function f(d) represents the initial radius of the algae when d = 0. In this case, the y-intercept is 9 mm.

C: To find the average rate of change of the function from d = 3 to d = 9, we need to find the difference in the radius of the algae at d = 9 and d = 3 and divide by the difference in the number of days.

f(9) = 9(1.04)^9 = 12.81 mm

f(3) = 9(1.04)^3 = 10.46 mm

Average rate of change = (12.81 - 10.46) / (9 - 3) = 0.71 mm/day

The average rate of change represents the average amount by which the radius of the algae increases each day from d = 3 to d = 9.