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? 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 = 3 to d = 9, and what does it represent?

A.) 9

B.) 9

C.) It represents a slope or gradient which is equal to 0.9

Step-by-step explanation:

A.) You are given the equation to show the radius of the algae, f(d), in mm, after d days: f(d) = 9(1.04)^d 

To find the domain, substitute 12.81 mm for function f(d) in the given equation.

12.81 = 9(1.04)^d

Divide both sides by 9

(1.04)^d = 12.81/9

(1.04)^d = 1.423333

Log both sides

Log (1.04)^d = log ( 1.423333)

d Log(1.04) = log(1.42333)

Make d the subject of formula

d = log(1.4233) / log(1.04)

d = 9

Therefore, the reasonable domain to plot the growth function is 9

B.) The y - intercept of the graph of the function f(d) is the initial radius of the algae which is represented by 9

C.) From the given function

F(d) = 9(1.04)^d

Substitute d for 3 and 9

The given value for f(d) when the domain d = 9 is 12.81

When d = 3

Substitute d for 3 into the formula

F(d) = 9(1.04)^3

F(d) = 9 × 1.124864

F(d) = 10.12

the average rate of change of the function will be

M = ( 10.12 - 12.81 ) / ( 3 - 6 )

M = - 2.686 / - 3

M = 0.895

M represent the slope or the gradient of the function.

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