Ali earns a salary of $8.20$8.20 per hour at the video rental store, for which he is paid bi-weekly. Occasionally, Ali has to work overtime (time more than 4040 hours but less than 7575 hours). For working overtime, he is paid time-and-a-half. Ali's salary is given by the functionS(t)=8.2t328+24.62(t−40)if0<t≤40if40<t≤75𝑆(𝑡)={8.2𝑡if0<𝑡≤40328+24.62(𝑡−40)if40<𝑡≤75where t is the time in hours, 0<t≤750<𝑡≤75.Step 2 of 3 : Find limt→40+S(t)lim𝑡→40+𝑆(𝑡).
Question
Ali earns a salary of 8.20 per hour at the video rental store, for which he is paid bi-weekly. Occasionally, Ali has to work overtime (time more than 4040 hours but less than 7575 hours). For working overtime, he is paid time-and-a-half. Ali's salary is given by the functionS(t)=8.2t328+24.62(t−40)if0<t≤40if40<t≤75𝑆(𝑡)={8.2𝑡if0<𝑡≤40328+24.62(𝑡−40)if40<𝑡≤75where t is the time in hours, 0<t≤750<𝑡≤75.Step 2 of 3 : Find limt→40+S(t)lim𝑡→40+𝑆(𝑡).
Solution
To find the limit as t approaches 40 from the right (40+) of the function S(t), we need to use the definition of the function for values of t greater than 40.
The function S(t) is defined as 328 + 24.62(t - 40) for values of t greater than 40.
So, we substitute t = 40 into this equation:
S(t) = 328 + 24.62(40 - 40) = 328 + 24.62 * 0 = 328 + 0 = 328
Therefore, the limit as t approaches 40 from the right of the function S(t) is 328.
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