Billy has a savings account and has written a function for the balance of the account f(t)=20t + 40?

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. 1. Interpreting the function. (3 points each)
2. a. Explain what the 20 represents in this situation.b. Explain what the 40 represents in this situation. 
3. 2. Complete the function table for Billy's account. (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

1. 3. Interpreting the table.
2. a. What is the pattern with column 3? (3 points)
3. b. What do the values in column 3 represent in terms of the situation? (3 points)
4. c. What do the values in column 3 represent in terms of the function? (3 points)
5. 4. Based upon the pattern in the table, is the function linear? Justify your answer using your answers to 3a, 3b, 3c. (6 points)
6.  

Answer 1

t f f(n+1)-f(n)

0 40 20

1 60 20

2 80 20

3 100 20

4 120 20

5 140 20

third column is the slope, the derivative of the function f'=20=slope

It's linear, because the slope is constant, because the exponent of t is 1. Graph it, it's a straight line 40 is the value of f(t) when t=0 which is the y intercept