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) = 11(1.01)°

Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm.
What is a reasonable domain tc plot the growth function?
(4 points)

Part B: What does the y-intercept of the graph of the function f(c) represent? (2 points)

Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points)

Answer 1

Explanation:

a.

f(d)=11(1.01^d

d=6.97 days

b.

t

f(c) represents the size of algae after c days

c.

f(2)=11(1.01)^2

f(7)=11(1.01)^7

`rate=(f(7)-f(2))/(7-2) \\=(11(1.01)^7-11(1.01)^2)/(5) \\=(11[(1.01)^7-(1.01)^2])/(5) \\\approx 0.0104 ~mm`