Question: Tony has $500 in his bank account. The table shows the amount B available in the account after t years. Choose the model and its equation which best fits the situation.
Time(t)
0
1
2
3
4
5
Balance($) (B)
500
530
560
590
620
650
A ) Exponential; B = 500 (1.06)t B ) Linear; B = 500 + 6t C ) Quadratic; B = 500t² D ) Linear; B = 500 + 30t
Steps to derive
1 Draw a scatter plot of the data.
2 You can see that the graph is a straight line.
3 Find two points on the line such as (0, 500) and (1, 530).
4m = y2-y1x2-x1 = 530-5001-0 = 30 [Find slope of the line.]
5 Using a y-intercept of 500 and a slope of m = 30, you can write an equation of the line.
6 B = mt + b [Write slope-intercept form.]
7 B = 30t + 500 [Substitute 500 for b and 30 for m.]
8 So, the linear model B = 500 + 30t fits the data. [Replace b with 500 and m with 30.]
