Billy has a savings account and has written a function for the balance of the account f(t)=20t + 40, where t is the time in weeks from today and f(t) represents the balance?

Question

Billy has a savings account and has written a function for the balance of the account f(t)=20t + 40, where t is the time in weeks from today and f(t) represents the balance of the account as a function of the time in weeks.

1. Interpreting the function. (3 points each)

1. a. Explain what the 20 represents in this situation.
2. b. Explain what the 40 represents in this situation.

2. Complete the function table for Billy's account (not this one, but the one below). (9 points)

Column 1	Column 2	Column 3
t	f(t)	Δf(t) or change in f(t)
0	40	-------------------------
1	60	f(1) - f(0) = 60 - 40 = 20
2		f(2) - f(1) =
3
4
5

3. Interpreting the table.

1. a. What is the pattern with column 3? (3 points)
2. b. What do the values in column 3 represent in terms of the situation? (3 points)
3. c. What do the values in column 3 represent in terms of the function? (3 points)

4. Based upon the pattern in the table, is the function linear? Justify your answer using your answers to 3a and 3b. (

Answer 1

$20 represents how much he saves each week. Graphically, it's the slope of the f(t) function or its derivative, f'(t), the function is an upward sloping straight line with minimum point (0,40)

$40 represents his beginning balance. Or graphically, 40 is the y intercept, when t=0. with t graphed on the horizontal or x axis

column

2 3

40 20

60 20

80 20

100 20

120 20

140 20

column 3 represents how much his savings account grows each week,

It grows $20 every week. In terms of the function it represents the slope or derivative f'(t)

the function is linear. If you graph it, it's a straight line. the function f(t) has only one variable with an exponent of 1.