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- laughoutloud

Help plz
Shannon manages a small zoo and she has been analyzing the attendance data. Shannon finds that the number of visitors increases exponentially as the temperature increases, and this situation is represented by the function f(x) = 3x. Shannon 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 + 4. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents.

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- laughoutloud

- katieb

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- laughoutloud

- phi

*** Find the solution to the two functions***
that is the point where the two curves cross.
can you read the (x,y) point where the two lines meet?

- laughoutloud

so I set it up as a set of solutions?
y=-x-4
y=3x

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- laughoutloud

or would it just be (1,3)

- phi

the "x" is an exponent in the 2nd equation and you should write it y= 3^x
or use the equation editor
\[ y= 3^x\]
but that is hard to solve. You may not have learned how.

- laughoutloud

no I haven't

- phi

If you can read the point, it is (1,3)
as a double check, for *both* equations, put in x=1
what do you get for y?
g(x) = −x + 4
g(1)= -1+4 = 3 which works
and
f(x)= 3^x
f(1)= 3^1 which means 3
so that works also.
(It's always good to double check when you read a graph.. )

- laughoutloud

Thank you so much :)

- phi

*** explain what the solution represents***
the solution means when the temperature rises exactly 1 degree
then the number of people arriving matches the number leaving

- laughoutloud

Ok! that makes a lot of sense thank you!

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