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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)
1300
1690
2197
Option 2 (amount in dollars)
1300
1600
1900

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)

Sagot :

quickersniffer69

Answer:

A)

For option 1, the type of function is linear because the series of interest earned increases arithmetically in $110 per year.

For option 2, the type of function is exponential because the series of interest earned increases geometrically in $1.09 per year.

b)

The option 1 refers to a simple interest with a function: f(n) = $1000 + $100n

The option 2 refers to a compound interest with a function: f(n) = $1000 * (1.09)ⁿ

c)

After 20 years, she would get:

in option 1, f(20) = $1000 + $110*20 = $3200

in option 2, f(20) = $1000 * (1.09)²⁰ = $5604.41

There is a significant difference between these options because the interest earned (through compound interest) ACCRUES on the principal amount and the accumulated interest of previous periods.

Step-by-step explanation:

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