1. 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)

(10 points)

2. The price of fuel may increase due to demand and decrease due to overproduction. George is studying the change in the price of two types of fuel, A and B, over time.

The price f(x), in dollars, of fuel A after x months is represented by the function below:

f(x) = 2.27(0.88)x

Part A: Is the price of fuel A increasing or decreasing and by what percentage per month? Justify your answer. (5 points)

Part B: The table below shows the price g(m), in dollars, of fuel B after m months.

m (number of months) 1 2 3 4
g(m) (price in dollars) 3.44 3.30 3.17 3.04
Which type of fuel recorded a greater percentage change in price over the previous month? Justify your answer. (5 points)

(10 points)

3. Autumn is thinking about buying a car for $38,000. The table below shows the projected value of two different cars for three years.

Number of years 1 2 3
Car 1 (value in dollars) 32,000 26,000 20,000
Car 2 (value in dollars) 32,300 27,455 23,336.75

Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)

Part B: Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)

Part C: Autumn wants to purchase a car that would have the greatest value in 5 years. Will there be any significant difference in the value of either car after 5 years? Explain your answer, and show the value of each car after 5 years. (4 points)

(10 points)