anonymous
  • anonymous
Jake is looking over some data regarding the strength, measured in Pascals (Pa), of some building materials and how the strength relates to the length. The data are represented by the exponential function f(x) = 2x, where x is the length. Explain how he can convert this equation to a logarithmic function when strength Pascals.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
jim_thompson5910
  • jim_thompson5910
x is the length, what is f(x)?
anonymous
  • anonymous
y?

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jim_thompson5910
  • jim_thompson5910
in terms of the word problem
anonymous
  • anonymous
the strength in terms of the length
jim_thompson5910
  • jim_thompson5910
yes, x = length, f(x) = strength
jim_thompson5910
  • jim_thompson5910
so when they say `strength is 8 Pascals.` we can replace `f(x)` with `8`
anonymous
  • anonymous
8=2^x
jim_thompson5910
  • jim_thompson5910
now convert that to a log equation
anonymous
  • anonymous
Ok:) is it log 2x =8?
jim_thompson5910
  • jim_thompson5910
I think you mean \[\Large \log_2(x) = 8\] right? you're close but not quite there
anonymous
  • anonymous
yes! Something along those lines
jim_thompson5910
  • jim_thompson5910
you'll use the rule \[\Large b^x = y \ \ \implies \ \ \log_b(y) = x\]
anonymous
  • anonymous
Ok thank-you :)!!
anonymous
  • anonymous
what about the 8 pascals?
jim_thompson5910
  • jim_thompson5910
how would you use that rule to rewrite \[\Large 2^x = 8\]
anonymous
  • anonymous
Look at base b^x=y as if it were 2^x=8
anonymous
  • anonymous
Now look at the log equation and replace each variable with the corresponding one.
jim_thompson5910
  • jim_thompson5910
yeah so b = 2 and y = 8
anonymous
  • anonymous
That's it right?
jim_thompson5910
  • jim_thompson5910
what log equation do you have now
anonymous
  • anonymous
2^x = 8 means log(base 2) 8 = x
jim_thompson5910
  • jim_thompson5910
good
anonymous
  • anonymous
That's it then?
jim_thompson5910
  • jim_thompson5910
yeah \[\Large 2^x = 8\] turns into \[\Large \log_2(8) = x\]
anonymous
  • anonymous
Thank you so much~~!!
anonymous
  • anonymous
I have one more?
jim_thompson5910
  • jim_thompson5910
go ahead
jim_thompson5910
  • jim_thompson5910
what are your thoughts?
anonymous
  • anonymous
it's suppose to be 50^x. Sorry!
anonymous
  • anonymous
I would tell her to convert it. I dont know which formula to use now though
jim_thompson5910
  • jim_thompson5910
you'd use the one I just posted. The rule going from exponential to log
anonymous
  • anonymous
Ok. Lemme try it
anonymous
  • anonymous
log 50 (17)=x
jim_thompson5910
  • jim_thompson5910
yes, \[\Large \log_{50}(17) = x\]
anonymous
  • anonymous
That's it? It was that simple?
jim_thompson5910
  • jim_thompson5910
here is a pic that has an alternate route http://ashikmdigitalportfolio.weebly.com/uploads/1/9/2/5/19253115/8805020_orig.jpg?146 either method gets the same answer
anonymous
  • anonymous
Thank you!!!
anonymous
  • anonymous
Can I ask one last question? Pleasee?
jim_thompson5910
  • jim_thompson5910
sure
anonymous
  • anonymous
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.
anonymous
  • anonymous
Ty!
jim_thompson5910
  • jim_thompson5910
it says `The graph of the two functions is below` where do the two functions cross?
anonymous
  • anonymous
oh hold on! I can graph it
anonymous
  • anonymous
http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIzXngiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjAsImVxIjoiLXgrNCIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MTAwMH1d
jim_thompson5910
  • jim_thompson5910
looks good
jim_thompson5910
  • jim_thompson5910
where do the two functions cross?
anonymous
  • anonymous
at (1,3)
jim_thompson5910
  • jim_thompson5910
what does that point mean?
anonymous
  • anonymous
It is the solution?
jim_thompson5910
  • jim_thompson5910
it's the solution to the system, yes but what does that solution mean in terms of the word problem?
anonymous
  • anonymous
The number of people who leave the park early due to the temperature?
jim_thompson5910
  • jim_thompson5910
let's go back to each function one by one f(x) = 3^x what is x? what is f(x)?
anonymous
  • anonymous
umm the increase in temperature for f(x)?
jim_thompson5910
  • jim_thompson5910
for f(x) = 3^x x = temperature f(x) = number of visitors
jim_thompson5910
  • jim_thompson5910
how about g(x) = -x+4 ?
anonymous
  • anonymous
-x=temperature or people leaving?
jim_thompson5910
  • jim_thompson5910
x looks like the change in temp
anonymous
  • anonymous
yes
anonymous
  • anonymous
hmm..is that when the temperature and # of people are equal?
anonymous
  • anonymous
Wait! NVM haha
jim_thompson5910
  • jim_thompson5910
so what I'm thinking is that when x = 1, the temperature change is 1 degree so as the temp increases by 1, the number of visitors is 3 (maybe 3 thousand or something) also, when x = 1, the number of people who leave early is 3 (thousand?) this problem is a bit odd
anonymous
  • anonymous
I know right? Ugh!!! So, would (1,3) mean that that's the temp. needed to have the most visitors?
jim_thompson5910
  • jim_thompson5910
maybe it's when the temp change is +1, then the number of visitors equals the number of people who leave early
jim_thompson5910
  • jim_thompson5910
what's strange is that I don't see how you can get more visitors growing forever if it's like 100+ degrees. If anything, the attendance would go down
anonymous
  • anonymous
Oh! I didn't look at it that way! That is strange.
anonymous
  • anonymous
It's a poorly worded question tbh
jim_thompson5910
  • jim_thompson5910
yeah I agree
anonymous
  • anonymous
i'm going to go with your answer :)
anonymous
  • anonymous
Thanks so much for all your help today!!! You're awesome :D
jim_thompson5910
  • jim_thompson5910
sure thing

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