Utility companies usually charge their customers based on the number of kilowatt-hours their customers consume in a period. Suppose the function A(p)=0.096p+19.50 represents the monthly charge, A, in dollars for a customer with Electric Company A consuming p kilowatt-hours of power. The function B(p)=0.104p+17.75 represents the monthly charge, B, in dollars for a customer with Electric Company B consuming p kilowatt-hours of power. Analyze the functions by interpreting the slope and y-intercept for each function in terms of the context for this situation. Then assess how the slope and y-intercept of Electric Company A compare with the slope and y-intercept of Electric Company B in this situation.
so whats the answer I've tried that and I'm still rly confused
Utility companies usually charge their customers based on the number of kilowatt-hours their customers consume in a period. Suppose the function A(p)=0.096p+19.50 represents the monthly charge, A, in dollars for a customer with Electric Company A consuming p kilowatt-hours of power. The function B(p)=0.104p+17.75 represents the monthly charge, B, in dollars for a customer with Electric Company B consuming p kilowatt-hours of power. Analyze the functions by interpreting the slope and y-intercept for each function in terms of the context for this situation. Then assess how the slope and y-intercept of Electric Company A compare with the slope and y-intercept of Electric Company B in this situation.
did not mean to do that
What's the "p" in "0.096p" meaning?
To analyze the functions A(p) and B(p), let's start by interpreting the slope and y-intercept in the context of this situation.
For function A(p)=0.096p+19.50:
- Slope (0.096): The slope represents the rate of change or cost per kilowatt-hour. In this case, Electric Company A charges $0.096 per kilowatt-hour consumed.
- Y-intercept (19.50): The y-intercept represents the fixed cost or base charge that the customer must pay regardless of their power consumption. In this case, even if the customer consumes zero kilowatt-hours, they will still have to pay $19.50.
For function B(p)=0.104p+17.75:
- Slope (0.104): Similarly, the slope represents the rate of change or cost per kilowatt-hour. Electric Company B charges $0.104 per kilowatt-hour consumed.
- Y-intercept (17.75): The y-intercept is the fixed cost or base charge. In this case, regardless of the power consumption, the customer will have to pay $17.75.
Now, let's assess how the slope and y-intercept of Electric Company A compare with Electric Company B:
- Slope comparison: The slope of Electric Company A is 0.096, while the slope of Electric Company B is 0.104. This indicates that Electric Company B charges a higher rate per kilowatt-hour consumed compared to Electric Company A. Therefore, for the same consumption, the cost with Electric Company B will be higher.
- Y-intercept comparison: The y-intercept of Electric Company A is $19.50, while Electric Company B has a y-intercept of $17.75. This implies that Electric Company A has a higher fixed cost or base charge compared to Electric Company B. Therefore, even with zero power consumption, customers of Electric Company A will have to pay a higher base charge than those with Electric Company B.
In summary, Electric Company A has a lower slope (lower rate per kilowatt-hour) but a higher y-intercept (higher fixed cost) than Electric Company B. This means that Electric Company A provides a lower rate per kilowatt-hour consumed, but customers will have to pay a higher fixed cost compared to Electric Company B.
recall the slop-intercept form for a line: y = mx+b
m is the slope. So, compare the coefficient of p in your two functions, as they are the slopes.
The y-intercept is just the value of the function when no power has been used (p=0)