Question

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. (4 points) (10 points)

Answer 1

Answer:

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. (4 points) (10 points)

Step-by-step explanation:

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. (4 points) (10 points)

Answer 2

A: Linear and exponential functions can be used to describe the value of the investment after a fixed number of years

B. $A = P + 100t$, $A = P*1.1^t$

C: Yes, there will be a significant difference

Explanation:

PART A.

• Option 1 allows you to characterise the investment's worth after a defined number of years using a linear function.
• This is because the total under Option 1 rises by a predetermined amount each year.
• In the case of option 2, the exponential function may be used to describe the value of an investment after a particular number of years.
• This is due to the fact that the growth in Option 2 this year is greater than the prior year.

Part B.

• For the first option, the function is $A = P + 100t$
• For the second option,  the function is $A = P*1.1^t$

Part C.

• There shall be a significant difference after 20 years
• Option 1 shall yield $3000
• Option 2 shall yield $6727.50
• There is a difference of $3527.50 on a principal investment of 1000 dollars.