Question

Question 1 (Essay Worth 10 points)(03.03 MC)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)dPart 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? (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 = 2 to d = 7, and what does it represent? (4 points)                Source                  StylesFormat ◢ Question 2 (Essay Worth 10 points)(03.02, 03.03, 03.04 MC)The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Marco is studying the change in the amount of money in two accounts, A and B, over time.The amount f(x), in dollars, in account A after x years is represented by the function below:f(x) = 1,264(1.09)xPart A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)Part B: The table below shows the amount g(r), in dollars, of money in account B after r years:r (number of years)1234g(r) (amount in dollars)1,3751,512.501,663.751,830.13Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer. (5 points)

Answer 1

A biologist studying the growth of a particular species of algae and later designed a model equation for the growth

F(d) = 11(1.01)d

Where, f(d) is in mm and d is days

QUESTION A

F(d) = 11(1.01)d

f(d) = 11.79 mm

Substitute f(d) = 11.79 mm into the model equation

11.79 = 11(1.01)d

11.79 = 11 * 1.01 * d

11 .79 = 11.11 x d

11.79 = 11.11d

Divide both sides by 11.11

11.79/11.11 = 11.11d/11.11

d = 11.79/11.11

d = 1.061

Thde reasonable domain to plot the growth function is 1.061 < d > 1.061