Question

Hillel is juggling flaming torches to raise money for charity. His initial appearance raises $500, and he raises $15 for each minute of juggling performance. The amount of money Hillel raises is a function of the length of his performance in minutes. Write the function's formula.

r=500+15t

Answer 1

The function representing the amount Hillel raises is r = 500 + 15t, with 500 as the initial amount and 15 as the rate raised per minute of juggling.

Step-by-step explanation:

The function that represents the amount of money Hillel raises for charity as a function of the length of his performance in minutes is r = 500 + 15t. In this linear equation, 500 represents the initial amount raised by Hillel's appearance before he begins juggling, and it is the y-intercept of the function. The coefficient 15 represents the rate at which money is raised per minute of juggling, which is the slope of the line. Thus, for every additional minute of performance, Hillel raises an additional $15.

Considering a similar example for reference, Svetlana's tutoring earnings can be represented by the equation y = 25 + 15x, where 25 is the initial one-time fee and 15 is the amount earned per hour of tutoring. Similarly to Hillel's function, Svetlana's equation reflects a starting amount (y-intercept) and a rate of earning per unit of time (slope).