Use the following formula. \[ \mathrm{P}=\frac{\mathrm{P}\left[\left(1+\frac{\mathrm{r}}{\mathrm{n}}\right)^{\mathrm{nt}}-1\right]}{\left(\frac{r}{n}\right)} \] Suppose that you drive 50,000 miles per year and gas averages \( \$ 4 \) per gallon. Complete parts a. and \( \mathbf{b} \). below. a. What will you save in annual fuel expenses by owning a hybrid car averaging 50 miles per gallon rather than an SUV averaging 25 miles per gallon? \( \$ \) \$

To figure out your savings in annual fuel expenses by owning a hybrid car versus an SUV, let's break it down step by step. 1. **Calculate the gallons of gas used for the SUV**: - Total miles driven in a year: 50,000 miles - Fuel efficiency of the SUV: 25 miles per gallon - Gallons used by the SUV = Total miles / Fuel efficiency = \( 50,000 \, \text{miles} / 25 \, \text{mpg} = 2,000 \, \text{gallons} \) 2. **Calculate the annual fuel cost for the SUV**: - Cost of gas: $4 per gallon - Annual fuel cost for the SUV = Gallons used × Cost per gallon = \( 2,000 \, \text{gallons} \times 4 \, \text{\$} = \$ 8,000 \) 3. **Calculate the gallons of gas used for the hybrid**: - Fuel efficiency of the hybrid: 50 miles per gallon - Gallons used by the hybrid = Total miles / Fuel efficiency = \( 50,000 \, \text{miles} / 50 \, \text{mpg} = 1,000 \, \text{gallons} \) 4. **Calculate the annual fuel cost for the hybrid**: - Annual fuel cost for the hybrid = Gallons used × Cost per gallon = \( 1,000 \, \text{gallons} \times 4 \, \text{\$} = \$ 4,000 \) 5. **Calculate the savings**: - Savings = Annual fuel cost for SUV - Annual fuel cost for hybrid = \( 8,000 \, \$ - 4,000 \, \$ = 4,000 \, \$ \) So, the savings in annual fuel expenses by owning a hybrid car rather than an SUV is **\$4,000**. b. If you would like to ask about further calculations or similar comparisons, feel free to reach out!