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) = 7(1.06)d

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?

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

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?

Answer 1

Let's solve for d.

fd=(7)(1.06)d

Step 1: Add -7.42d to both sides.

df+−7.42d=7.42d+−7.42d

df−7.42d=0

Step 2: Factor out variable d.

d(f−7.42)=0

Step 3: Divide both sides by f-7.42.

d(f−7.42)f−7.42=0f−7.42

d=0f−7.42

Answer:

d=0f−7.42

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