The cost of a car service us partly constant and partly varies with the time it takes to do the work. It costs #3500 for a 5 and half hours service and #2900 for a 4 hours service, find the formula connecting cost, #C You with time, T hours.
c = b + r t
3500 = b + r (5.5)
2900 = b + r (4.0)
-------------------------- subtract
600 = 1.5 r
r = 400
go back and get b
C=a+bT(where a and b are constant). 3500=a+5.5b......(1). 2900=a+4b.........(2) (2)-(1). 600=1.5b. b=600/1.5
b=400.
Substitute b=400 in equation (1)
3500=a+5.5(400)
3500=a+2200
a=1300
Therefore, the formula connecting cost (C) with time (T) is:
C=1300+400T
To find the formula connecting the cost, C, with time, T in hours, we need to determine the constant cost and the rate of change of cost with respect to time.
Let's first determine the constant cost. We can do this by subtracting the varying cost from the total cost for the longer service:
Constant cost = Total cost - Varying cost
Constant cost = #3500 - #2900
Constant cost = #600
Now, let's find the rate of change of cost with respect to time. We can do this by dividing the change in cost by the change in time for the two given services:
Rate of change of cost = (Total cost for 5.5-hour service - Total cost for 4-hour service) / (Time for 5.5-hour service - Time for 4-hour service)
Rate of change of cost = (#3500 - #2900) / (5.5 - 4)
Rate of change of cost = #600 / 1.5
Rate of change of cost = #400 per hour
Now that we have the constant cost (#600) and the rate of change of cost per hour (#400), we can form the formula connecting cost, C, with time, T:
C = Constant cost + Rate of change of cost * T
C = #600 + #400 * T
Therefore, the formula connecting cost, C, with time, T, is C = #600 + #400T.