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)^d Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function?
Part B: What does the y-intercept of the function f(d) represent?
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?

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Part A: A reasonable domain of the growth function is 0 < d < 7

Part B: The y-intercept represents the starting radius of the algae which is 11 mm

Part C: (i) The average rate of change of the function from day 2 to day 7 ≈ 0.0698

(ii) The average rate of change represents the algae growth rate in mm/day, from day 2 to day 7

Step-by-step explanation:

Part A:

The given function that represents the radius of the algae is presented as follows;

f(d) = 11·(1.01)^d

Where;

f(d) = The radius of the algae

d = The time in days of growing of the algae

The radius of the algae at the time the biologist concluded her study = 11.79 m

Therefore, we have;

11.79 = 11 × (1.01)^d

(1.01)^d = 11.79/11 = 1179/1100

d = ㏑(1179/1100 )/(㏑1.01) ≈ 6.97

d ≈ 6.97 days

Therefore;

A reasonable domain of the growth function is 0 < d < 7 which is 1 week

Part B: The y-intercept of the function is the value of the function f(d), where the time d = 0

Therefore, the y-intercept represents the starting radius of the function, which gives;

f(0) = 11 × (1.01)⁰ = 11

The starting radius of the algae = 11 mm

Part C: (i) The average rate of change of the function from d = 2 to d = 7, A(is given as follows;

Therefore;

The average rate of change of the function from day 2 to day 7 ≈ 0.0698

(ii) The average rate of change represent the growth rate of the algae in mm/day, from day 2 to day 7 when the relationship is assumed to be linear

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step-by-step explanation: