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Erin earns a salary of $11.30$⁢11.30 per hour at the coffee shop, for which she is paid bi-weekly. Occasionally, Erin has to work overtime (time more than 4545 hours but less than 7070 hours). For working overtime, she is paid time-and-a-half. Erin's salary is given by the functionS(t)=11.3t508.5+33.92(t−45)if0<t≤45if45<t≤70𝑆(𝑡)={11.3𝑡if0<𝑡≤45508.5+33.92(𝑡−45)if45<𝑡≤70where t is the time in hours, 0<t≤700<𝑡≤70.Step 2 of 3 :  Find limt→45+S(t)lim𝑡→45+⁡𝑆(𝑡).

Question

Erin earns a salary of 11.3011.30⁢11.30 per hour at the coffee shop, for which she is paid bi-weekly. Occasionally, Erin has to work overtime (time more than 4545 hours but less than 7070 hours). For working overtime, she is paid time-and-a-half. Erin's salary is given by the functionS(t)=11.3t508.5+33.92(t−45)if0<t≤45if45<t≤70𝑆(𝑡)={11.3𝑡if0<𝑡≤45508.5+33.92(𝑡−45)if45<𝑡≤70where t is the time in hours, 0<t≤700<𝑡≤70.Step 2 of 3 :  Find limt→45+S(t)lim𝑡→45+⁡𝑆(𝑡).

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Solution

To find the limit as t approaches 45 from the right (denoted as t→45+), we use the second part of the piecewise function, as this part applies for t values greater than 45.

The function is S(t) = 508.5 + 33.92(t - 45).

We substitute t = 45 into this function:

S(45) = 508.5 + 33.92(45 - 45) = 508.5 + 33.92(0) = 508.5

So, lim(t→45+) S(t) = 508.5.

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