The local water company uses the following function for computing their customers' monthly water bills.C(x)={1.09x+3.116.82x−4007.89if0<x≤700ifx>700𝐶(𝑥)={1.09𝑥+3.11if0<𝑥≤7006.82𝑥−4007.89if𝑥>700, where x is the number of gallons used and C(x)𝐶(𝑥) is the cost in dollars.Step 1 of 3 : Find limx→700−C(x)lim𝑥→700−𝐶(𝑥).
Question
The local water company uses the following function for computing their customers' monthly water bills.C(x)={1.09x+3.116.82x−4007.89if0<x≤700ifx>700𝐶(𝑥)={1.09𝑥+3.11if0<𝑥≤7006.82𝑥−4007.89if𝑥>700, where x is the number of gallons used and C(x)𝐶(𝑥) is the cost in dollars.Step 1 of 3 : Find limx→700−C(x)lim𝑥→700−𝐶(𝑥).
Solution
To find the limit of the function C(x) as x approaches 700 from the left (denoted as lim(x→700-) we use the first piece of the piecewise function because this piece is valid for x values less than or equal to 700.
The first piece of the function is C(x) = 1.09x + 3.11.
Substitute x = 700 into this function:
C(700) = 1.09(700) + 3.11 = 763.11
So, lim(x→700-)C(x) = 763.11
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