Math

1.A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:

f(n) = 12(1.03)n

Part A: When the scientist concluded his study, the height of the plant was approximately 16.13 cm. 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(n) represent? (2 points)

Part C: What is the average rate of change of the function f(n) from n = 3 to n = 10, and what does it represent? (4 points)

2.The price of products may increase due to inflation and decrease due to depreciation. Derek is studying the change in the price of two products, A and B, over time.

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

f(x) = 72(1.25)x

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

Part B: The table below shows the price f(t), in dollars, of product B after t years:

t (number of years)
1 2 3 4

f(t) (price in dollars)
65 84.5 109.85 142.81

Which product recorded a greater percentage change in price over the previous year? Justify your answer.

3.Belinda wants to invest $1000. The table below shows the value of her investment under two different options for three different years:

Number of years
1 2 3

Option 1 (amount in dollars)
1100 1210 1331
Option 2 (amount in dollars) 1100 1200 1300

Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)

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

Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option.

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