Mike is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation.

- anonymous

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- phi

if you have "x" as an exponent, use log to "get at the x"

- phi

\[ 37^x = 12 \]
first, "take the log" of both sides.
\[ \log(37^x) = \log(12) \]
any idea what you can do now?

- anonymous

@phi

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- phi

x= log 12/log 37
if we use log base 10 (it does not matter what base we use)
x= 1.079181246/1.5682017 = 0.688164812

- phi

type into google
37^0.688164812 =

- anonymous

So log 12= 1.079 and log 37= 1.568 and you just divide to get the answer?

- phi

you get 12 (if you round it)
**So log 12= 1.079 and log 37= 1.568 and you just divide to get the answer?***
yes, but use as many digits as the calculator has. You need lots of digits to get a close answer when using log or exponents.

- anonymous

Okay can you please help me with two more I really need to pass!

- phi

ok

- anonymous

Wendy is looking over some data regarding the strength, measured in Pascals (Pa), of some rope and how the strength relates to the number of woven strands in the rope. The data are represented by the exponential function f(x) = 2x, where x is the number of woven strands. Explain how she can convert this equation to a logarithmic function when strength is 256 Pascals.

- phi

This was an earlier question. It is not very clear, as written, but they say
" data regarding the strength"
"data are represented by the exponential function "
means
"strength is given by this function"

- phi

so I would write
strength in Pascals = f(x) = 2^x
and thus
2^x = 256 Pascals

- anonymous

Kylee manages a small theme park and she has been analyzing the attendance data. Kylee finds that the number of visitors increases exponentially as the temperature increases, and this situation is represented by the function f(x) = 4x. Kylee 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 + 5. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents.

##### 1 Attachment

- phi

any thoughts on this one?

- phi

btw, you mean "and it is represented by **g(x)** = −x + 5." not f(x)

- anonymous

I have no idea where to start this one is my hardest.

- anonymous

And I just put what the question asked so I don't think it is g(x) maybe it is a question typo though.

- phi

It's a typo. First, you don't give two different functions the same name. The first one is called f(x), so you would not call the 2nd one f(x). Total confusion if you do that.
Also, on the graph, they label the line g(x) (a big hint the question should also so g(x))

- anonymous

It looks like you are correct on second looking it is a typo so how do I write this?

- phi

they tell you (let's use g(x) )
"a linear equation that models the number of people who leave early
depending on the change in temperature"
and then they give you the equation for a line
g(x) = -x + 5
you "put in x" and get out (presumably) the number of people leaving

- phi

what does "x" represent ? any idea ?

- anonymous

I think x represents the number of people but Im not sure

- phi

what you get out is the number of people leaving.
in other words g(x) is a formula that tells you how many people leave when x is some number. What is "x" ? read this again:
"a linear equation that models the number of people who leave early depending on the change in temperature"

- anonymous

So x is the change in temperature?

- phi

yes. It sounds a bit goofy... but it is a made up problem. If the temperature changes 1 degree (this part is goofy... 1 degree from when or what?). But anyway, if the temperature changes by 1 degree then g(1) tells us
g(1) = -1 + 5 = 4
4 people leave early

- anonymous

I get it now, but what would I put as the answer?

- phi

f(x) is a formula that tells how many people arrive.
the point where the two curves cross is where the number of people coming equals the number leaving, and the number of people in the park is constant (number coming in matches going out)

- anonymous

So what would I put as the answer? I know I'm kinda slow but please bear with me.

- anonymous

Yes....

- phi

can you read off the (x,y) numbers?

- anonymous

Of where it crosses?

- phi

yes, where they cross

- anonymous

1,4

- anonymous

am i right? (1,4)

- phi

so (1,4) is the solution
to the "two curves"
it is the one point the lies on both curves.
In this case, it means at x=1 (i.e. when the temperature goes up by 1 degree),
the number of people coming and the number leaving are both 4
this means the number of people in the park is not changing.

- phi

ok, but the last sentence is not quite right. x represents the change in temperature.
the "solution" to the two functions is (1,4)

- anonymous

So just change the last sentence to the solution represents the change in temperature?

- phi

I would remove the last sentence, and put up front
"the solution is (1,4)"
and then the rest explains what that means

- anonymous

Okay thank you so much you were a great help and I will surely write a fan testimonial for you.

- phi

yw

- anonymous

Hey @phi ....

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