Question

***FAN AND MEDAL***

Steve manages a skate park and he has been analyzing the attendance data. Steve finds that the number of visitors increases exponentially as the temperature increases, and this situation is represented by the function f(x) = 5x. Steve also finds a linear equation that models the number of people who leave the park early depending on the change in temperature, and it is represented by f(x) = −x + 6. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents.

Answer 1

It's important that you express your exponential function here as \[f(x) = 5^x\]

Answer 2

Oh ok thank you I totally forgot

Answer 3

Otherwise one would think you meant y = 5 times x.

Answer 4

so you have two functions, which are to be graphed on the same set of coordinate axes.
We need to determine the coordinates of the 2 points at which the 2 graphs intersect.

Answer 5

Have you graphed expo functions such as y = 5^x before?

Answer 6

I have a picture but I cannot access it, i know that the two graphs intersect at (1,5)

Answer 7

Table of values

x f(x)=5^x

0 1
1 5
2 25

and so on.

Have to graph the straight line also.

Answer 8

If x=0, y=5^0= 1
1 5
2 25
3 125

Answer 9

It is y = -x +6

Answer 10

Indeed it is. How would you normally graph a function such as this one and another such as y = 5^x?

Answer 11

In this case a very quick sketch may be all you need. What would the graph of y=-x+6 look like?

Answer 12

Its slope is:

Its y-intercept is:

Answer 13

The slope is 1 / -1 and the y int is 6

Answer 14

@yeval76: OpenStudy tells me you're working on a different problem (skate park). Still interested in finishing the current problem?

Answer 15

The slope is m=-1 and the y-intercept is (0,6).

Answer 16

yes the problem I am currently working on is the skate park problem

Answer 17

If you've used the Draw utility before, or wouldn't mind learning now, quickly sketch y=-x+6.