Question

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?

Answer 1

A) A reasonable domain to plot the growth function is; d = 9.02

B) The y-intercept of the function is; 9

C) The average rate of change of the function f(d) from d = 3 to d = 9 is; 0.4477

What is the domain of the function?

We are given the equation that shows the radius of the algae, f(d), in mm, after d days as; f(d) = 9(1.04)^(d)

A) We are told that the radius is approximately 12.81 mm. Thus;

9(1.04)^(d) = 12.81

(1.04)^(d) = 12.81/9

(1.04)^(d) = 1.4233

d * log 1.04 = log 1.4233

d = 0.1533/0.017

d = 9.02

B) The y-intercept is obtained when the domain is zero. Thus;

f(0) = 9(1.04)^(0)

f(0) = 9

C) Average rate of change is given by the formula;

f'(x) = [f(b) - f(a)]/(b - a)

from d = 3 to d = 9. Thus;

f'(x) = (f(9) - f(3))/(9 - 3)

f'(x) = (9(1.04)^(9) - 9(1.04)^(3))/6

f'(x) = 0.4477

Read more about Domain of function at; brainly.com/question/10197594

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