Electricity Rates in Florida Florida Power & Light Company...

Electricity Rates in Florida Florida Power \& Light Company supplies electricity to residential customers for a monthly customer charge of $\$ 8.01$ plus 8.89 cents per kilowatt hour (kWh) for up to 1000 kilowatt hours. (a) Write a linear equation that relates the monthly charge $C$, in dollars, to the number $x$ of kilowatt hours used in a month, $0 \leq x \leq 1000$. (b) Graph this equation. (c) What is the monthly charge for using 200 kilowatt hours? (d) What is the monthly charge for using 500 kilowatt hours? (e) Interpret the slope of the line.

Key Concepts

Linear Equations

A linear equation represents a relationship between two variables using a constant rate of change. In many contexts, such as cost estimation, the equation takes the form y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept. This form allows us to model scenarios where one quantity changes at a steady rate as the other increases.

Slope

The slope of a linear equation is a measure of the rate at which the dependent variable changes in relation to the independent variable. It quantifies the increase or decrease in y for each unit change in x, providing an interpretation of the marginal or variable component of a function, such as the incremental cost per unit consumed.

Y-Intercept

The y-intercept in a linear equation is the value of the dependent variable when the independent variable is zero. This constant term represents a fixed starting point of the relationship, often corresponding to a base charge or initial value that is independent of changes in the other variable.

Graphing Functions

Graphing a linear function involves plotting points that satisfy the equation and drawing a straight line through them. The graph visually represents the relationship between the variables, with the slope determining the line’s steepness and direction, and the y-intercept indicating where the line crosses the vertical axis.

Function Evaluation

Function evaluation is the process of substituting a specific value for the independent variable into the function to calculate the corresponding value of the dependent variable. This allows for practical application of the model, such as calculating the total cost at different levels of usage.

Transcript

00:01 Alright, so we are looking at electricity rates in florida for florida power and light and we discover or we're told that there's a flat charge of $8 .00 and a penny, $8 .01 for each month for a customer and then they charge by the cent for kilowatt hours.

00:20 So we've got the monthly charge in dollars and we've got the kilowatt hour charge in cents.

00:25 So the first thing we need to do is either change both to cents or both to dollars.

00:32 And since we're likely going to be dealing with larger numbers, i'm going to go ahead and change this $8 .89 to dollars.

00:40 So we're going to move the decimal two places to the left because there's 100 cents in a dollar.

00:46 So we just move the decimal two places to the left and add a zero.

00:50 And then the question says to write a linear equation that relates the monthly charge, c in dollars to the number of kilowatt hours.

01:01 So the cost per month is based on the number of kilowatt hours they use.

01:06 So c is the cost per month and x is the kilowatt hours.

01:13 So our cost is going to be .0889 times the number of kilowatt hours plus the $8 .01 each month.

01:27 So that's our equation.

01:28 C of x equals .0889 times x plus $8 .01.

01:35 And we're only going to do this between zero and 1000.

01:42 So x has to be greater than zero, can't be zero, i guess, greater than or equal to zero.

01:46 And it has to be less than or equal to 1000.

01:49 Then we want to graph this equation.

01:52 So we're going to go to your graphing tool and using our variable here.

02:11 So .0889x plus $8 .01.

02:14 Then that's what the graph looks like...

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