Final answer:
The given equation P=33+3.18w is a linear mathematical model relating Mackenzie's monthly water bill to the amount of water consumed. It shows a base fee of $33 plus $3.18 for each thousand gallons used. Similar models also exist for calculating electricity bills based on appliance usage and duration.
Step-by-step explanation:
The equation P=33+3.18w models the relationship between the monthly water bill payment, P, in dollars, and the amount of water used in a month by Mackenzie, w, in thousands of gallons. This linear equation suggests that Mackenzie's water bill payment will increase by $3.18 for each additional thousand gallons of water used, starting with a base fee of $33. This type of model is a practical example of how mathematics can be applied to everyday life situations such as calculating utility bills based on consumption.
Similar mathematical models are used to calculate other types of bills, such as electricity. The familiar fact that the more electric appliances you use and the longer they are left on, the higher your electric bill will be, is based on the relationship between energy and power. You pay for the energy used, as represented by another formula P = E/t, where P is power, E is energy, and t is time.