Beth earns a salary of $9.10$9.10 per hour at the cafeteria, for which she is paid monthly. Occasionally, Beth has to work overtime (time more than 3030 hours but less than 6565 hours). For working overtime, she is paid time-and-a-half. Beth's salary is given by the functionS(t)=9.1t273+27.32(t−30)if0<t≤30if30<t≤65𝑆(𝑡)={9.1𝑡if0<𝑡≤30273+27.32(𝑡−30)if30<𝑡≤65where t is the time in hours, 0<t≤650<𝑡≤65.Step 2 of 3 : Find limt→30+S(t)lim𝑡→30+𝑆(𝑡).
Question
Beth earns a salary of 9.10 per hour at the cafeteria, for which she is paid monthly. Occasionally, Beth has to work overtime (time more than 3030 hours but less than 6565 hours). For working overtime, she is paid time-and-a-half. Beth's salary is given by the functionS(t)=9.1t273+27.32(t−30)if0<t≤30if30<t≤65𝑆(𝑡)={9.1𝑡if0<𝑡≤30273+27.32(𝑡−30)if30<𝑡≤65where t is the time in hours, 0<t≤650<𝑡≤65.Step 2 of 3 : Find limt→30+S(t)lim𝑡→30+𝑆(𝑡).
Solution
To find the limit as t approaches 30 from the right (denoted as t→30+), we use the second part of the piecewise function, as this part applies for t values greater than 30.
The function is S(t) = 273 + 27.32(t - 30).
Substitute t = 30 into this function:
S(30) = 273 + 27.32(30 - 30) = 273 + 27.32(0) = 273.
So, lim(t→30+) S(t) = 273.
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