Question

Steve is managing a skate park and has been analyzing the attendance data. Steve has found that the number of visitors increases exponentially as the temperature increases. Steve has also found a linear equation that models the number of people who leave the park early depending on the temperature. Describe how Steve can combine these two functions into a new function and explain what that function would predict.

Answer 1

Alright, let's break this down into parts.

The first part comes from the statement: the number of visitors increases exponentially as the temperature increases. There are two variables, number of visitors and temperature, so we'll name them V and t, respectively. Since V increases exponentially with t, the formula for the equation relating the two is V = a^t, where a is some positive constant.

The second part comes from this statement: a linear equation models the number of people who leave depending on the temperature. So, we have two variables again, number of visitors and temperature, but to avoid confusion, we'll use L to represent the visitors leaving and keep t for temperature. A linear equation is usually in the form y=mx+b, so our version here is L = mt+b.

Now, the third part is putting the two previous parts together. The first part is the number of visitors coming into the park, and the second part is the number of visitors leaving the park. So, N, the total number of visitors, could be found by this equation: N = V - L. To write this as a function of temperature, we just replace V and L with their equivalents from the previous parts: N = a^t-(mt+b).

Answer 2

The information included in this question is the intellectual property of Florida Virtual School. Posting questions from any FLVS course and receiving answers is considered cheating.