Final answer:
To approximate the amount of revenue generated by the camp, use a linear function with the cost as the x-variable and the number of youth participants as the y-variable. The slope is -0.4, and the y-intercept is 184. The linear function is y = -0.4x + 184.
Step-by-step explanation:
To approximate the amount of revenue generated by the camp, we need to create a linear function using the given information. Let's use the cost of the camp as the x-variable and the number of youth participants as the y-variable. We know that the camp costs $160 and has 120 youth participants. We also know that for every $20 increase in price, the number of youth decreases by 8.
We can use this information to find the slope of the linear function. The slope is calculated by finding the change in the y-variable divided by the change in the x-variable. In this case, the change in the y-variable is -8 (negative because the number of youth decreases) and the change in the x-variable is $20. So the slope is -8/20 = -0.4.
Now we can use the slope-intercept form of a linear function, which is y = mx + b, where m is the slope and b is the y-intercept. We already have the slope (-0.4). To find the y-intercept, we substitute one set of values from the given information into the equation. Let's use the cost of $160 and the number of youth participants of 120. We have 120 = -0.4(160) + b. Solving for b, we get b = 120 - (-0.4)(160) = 120 + 64 = 184.
Therefore, the linear function that approximates the amount of revenue generated by the camp is y = -0.4x + 184, where x is the cost of the camp and y is the revenue generated.