1. **State the problem:** Calculate how much a waitress makes for a 4-hour and an 8-hour shift given the pay function $P(t) = 2.52t + 78$, where $t$ is the number of hours worked. 2. **Formula used:** The total pay $P(t)$ is given by the linear function: $$P(t) = 2.52t + 78$$ where $2.52$ is the hourly wage and $78$ is the fixed amount in tips. 3. **Evaluate for $t=4$ hours:** $$P(4) = 2.52 \times 4 + 78 = 10.08 + 78 = 88.08$$ So, for a 4-hour shift, the waitress makes $88.08$. 4. **Evaluate for $t=8$ hours:** $$P(8) = 2.52 \times 8 + 78 = 20.16 + 78 = 98.16$$ So, for an 8-hour shift, the waitress makes $98.16$. 5. **Summary:** - For 4 hours: $88.08$ - For 8 hours: $98.16$ This shows the total pay increases linearly with hours worked, plus a fixed tip amount.