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. part b: write one function for each option to describe the value of the investment f(n), in dollars, after n years. part c: belinda wants to invest in an option that would 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.

Part A: Option 1 is exponential because it does not increase by a constant rate. Option 2 is linear because it increases by a constant rate.  

Part B:

For option 1: a(b)^x

a=1000 and b=1100/1000=1.1

the function will be:f(n)=1000(1.1)^x

For option 2:

Since the price increases by $100 each year, its linear.

Here would be the function: f(n)=1000+100(n)

Part C: Invest for 20 years in option 1: Yes.

f(20)=1000(1.1)^20

=1.1^20=6.72750

=6.72750x1000

=6727.50

y=6727.50, which is the price of the investment in 20 years.

For option 2:

f(20)=1000+100(20)

=1000+2000

=3000, which is the price the of the investment in 20 years.

If she uses option 2 rather than option 1, she will loose $3727.5

this is the formula: v = the value of investment at the end of the time period

p = the principal amount (the initial amount invested)

r = the annual interest rate

n = the annual frequency of compounding (how many times a year interest is added)

t = the number of years the money is invested

^ means raise to the power of