Bridgette has $1,000 to invest. She has two different investment options, shown in the table below. Each option would give her a different value over three years.

Number of Years 1 2 3
Option A (amount in dollars) 1100 1200 1300
Option B (amount in dollars) 1100 1210 1331

Part A: What type of function, linear or exponential, would be best to describe the value of the investment over a fixed number of years using Option A? Explain your answer.

Part B: Write a function, a(t), to describe the value of the investment, in dollars, of Option A after t years.

Part C: What type of function, linear or exponential, would be best to describe the value of the investment over a fixed number of years using Option B? Explain your answer.

Part D: Write a function, b(t), to describe the value of the investment, in dollars, of Option B after t years.

Part E: Bridgette wants to invest in whichever option would increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Bridgette's investment after 20 years if she uses Option A over Option B? Explain your answer, and show the investment value after 20 years for each option.

Question

09-11-2020
Mathematics

contestada

Bridgette has $1,000 to invest. She has two different investment options, shown in the table below. Each option would give her a different value over three years.

Number of Years 1 2 3
Option A (amount in dollars) 1100 1200 1300
Option B (amount in dollars) 1100 1210 1331

Part A: What type of function, linear or exponential, would be best to describe the value of the investment over a fixed number of years using Option A? Explain your answer.

Part B: Write a function, a(t), to describe the value of the investment, in dollars, of Option A after t years.

Part C: What type of function, linear or exponential, would be best to describe the value of the investment over a fixed number of years using Option B? Explain your answer.

Part D: Write a function, b(t), to describe the value of the investment, in dollars, of Option B after t years.

Part E: Bridgette wants to invest in whichever option would increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Bridgette's investment after 20 years if she uses Option A over Option B? Explain your answer, and show the investment value after 20 years for each option.

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moistkatana moistkatana · Answer 1 · 2020-11-11T02:20:27+01:00

Answer/Step-by-step explanation:

Part A: The function that would best describe Option A is a linear function. This is because an increase in x would have a corresponding additive increase in y. With each increasing year, the value of Option A increases by $100. This is how we know Option A would be a linear function.

Part B: a(t) = y.

a(t) = a + 100t

Part C: The function that would best describe Option B is an exponential function. Unlike linear functions, an increase in x would have a corresponding multiplicative increase in y. Each value of Option B shares a common ratio of 1.1.

Part D: b(t) = y.

b(t) = b(1.1)^t

Part E: a(20) = a + 100(20)

1100 + 2000 = 3100

b(20) = b(1.1)^20

1100(1.1)^20

= 7400

There is definitely a significant difference between the value of Bridgette’s investment in both options. The difference between the values of each option after 20 years is 4300. Bridgette is better off using Option B if she wants more money at the end.

Hope this helps!