Belinda wants to invest $1000. The table below shows the value of her investment under two different options for two different years:
Number of years 1 2 3
Option 1 1300 1690 2197
Option 2 1300 1600 1900
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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)
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Can anyone help me?
If you are only dealing with two types of growth, i.e. exponential or linear, you can distinguish one from the other as follows.
1. Linear function
we take advantage of the property of linear functions of having a constant slope.
Given three points, calculate the slopes of the graph between points 1 and 2 (=m1) and that of m2 between points 2 and 3. If they are equal, then the graph is linear.
Example, given points (1,2),(2,4),(4,8)
Slope between first two points: m1=(y2-y1)/(x2-x1)=(4-2)/(2-1)=2
Slope between last two points: m2=(y2-y1)/(x2-x1)=(8-4)/(4-2)=2
Since they are equal, the graph of the three given points is linear.
2. Exponential function.
Use the property of exponential functions that the rate of growth is constant.
Rate of growth = (y2/y1)^(1/(x2-x1))
For example, we have three points, (0,1),(2,16),(5,1024)
Rate of growth between first two points=(16/1)^(1/(2-0))=16^(1/2)=4
Rate of growth between last two points=(1024/16)^(1/(5-2))=64^(1/3)=4
Since the rates of growth are the same, the given three points belong to a graph of exponential growth.
For more information, you could read up: