PLEASE HELP I WILL MARK BRAINLIEST
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)

A reasonable domain is d = 9 days

Step-by-step explanation:

Given:

The equation to show the growth of algae's radius is given as:

f(d) = 9(1.04)^d

Where, 'd' represents the number of days passed. So, it represents the domain of the given function f(d).

f(d) is the function representing the radius of algae after 'd' days.

Now, the radius of algae given after 'd' days = 12.81 mm

Therefore, plug in 12.81 for  f(d). This gives,

12.81=9(1.04)^dfrac{12.81}{9}=(1.04)^dtextrm{Taking log on both the sides, we get:}log (\frac{12.81}{9})=\log(1.04)^dtextrm{Using log property} \log a^b=b\log a \therefore \log (\frac{12.81}{9})=d\times\log(1.04)d=\frac{\log (\frac{12.81}{9})}{\log(1.04)}d=9\ days

Therefore, after 9 days, the radius of algae is 12.81 mm.

I hope I helped!