Question

Santa's Wonderland is an extravagant holiday light display that is open from early November through January each year. The entry fee is $15 per vehicle for up to and including 5 people, with an additional $1.50 for each extra person. Express this information as a piecewise function of x, where x represents the number of people in the vehicle.

Can you please explain to me how you got the answer?

Answer 1

The entry fee for Santa's Wonderland can be represented as a piecewise function of the number of people in the vehicle.

Step-by-step explanation:

The information provided can be expressed as a piecewise function of x to represent the entry fee for Santa's Wonderland. Let's define the function as follows:

f(x) = 15 + 1.5(x-5) if x > 5

f(x) = 15 if 1 <= x <= 5

Here's how I got the answer:

1. If the number of people in the vehicle is greater than 5, we take the base fee of $15 and add $1.5 for each extra person. So, the function is f(x) = 15 + 1.5(x-5).
2. If the number of people in the vehicle is between 1 and 5 (inclusive), we only charge the base fee of $15. So, the function is f(x) = 15.

This piecewise function takes into account different scenarios based on the number of people in the vehicle and provides an accurate representation of the entry fee for Santa's Wonderland.

Answer 2

lets use slope-intercept formula, beacuse this problem looks linear.since this is a function we should use f(x) instead of y, so our equation should be f(x) = mx + b (it is usually y = mx+b). our slope would be 1.50 because it increases by a certain amount, and our y intercept would 15, since that is the initial amount, so our equation would be f(x) = 1.50x + 15 ( i think) so to find , lets say how much ten people could ride, then we would do 1.50(5) + 15 ( it is 5 and not 10 because remember 15 for up to and only 5 so just take of 5 from 10 and it five) and your answer would be $22.50 (in dollars) for 10 people.
hope this helps, sorry about the mistakes though.