Li earns a salary of 6.80 per hour at the video re

Questions: Li earns a salary of 6.80 per hour at the video rental store, for which he is paid bi-weekly. Occasionally, Li has to work overtime (time more than 40 hours but less than 70 hours). For working overtime, he is paid time-and-a-half. Li's salary is given by the function S(t) = 6.8 t if 0<t ≤ 40 272 + (20.4/2)(t-40) if 40<t ≤ 70 where t is the time in hours, 0<t ≤ 70. Step 1 of 3 : Find lim t→10^- S(t).

Transcript text: Li earns a salary of $\$ 6.80$ per hour at the video rental store, for which he is paid bi-weekly. Occasionally, Li has to work overtime (time more than 40 hours but less than 70 hours). For working overtime, he is paid time-and-a-half. Li's salary is given by the function \[ S(t)=\left\{\begin{array}{ll} 6.8 t & \text { if } 0

Solution

Solution Steps

Step 1: Identify the Relevant Function

For $ t $ approaching $ 10 $ from the left, we use the first piece of the piecewise function defined as: \[ S(t) = 6.8t \quad \text{for } 0 < t \leq 40 \]

Step 2: Evaluate the Function

Substituting $ t = 10 $ into the function, we calculate: \[ S(10) = 6.8 \times 10 \]

Step 3: Calculate the Result

Performing the multiplication gives: \[ S(10) = 68.0 \]

Thus, the limit $ \lim_{t \rightarrow 10^{-}} S(t) = 68.0 $.