Question

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.

Answer 1

@jim_thompson5910

Answer 2

x is the length, what is f(x)?

Answer 3

y?

Answer 4

in terms of the word problem

Answer 5

the strength in terms of the length

Answer 6

yes, x = length, f(x) = strength

Answer 7

so when they say `strength is 8 Pascals.`

we can replace `f(x)` with `8`

Answer 8

8=2^x

Answer 9

now convert that to a log equation

Answer 10

Ok:) is it log 2x =8?

Answer 11

I think you mean \[\Large \log_2(x) = 8\] right? you're close but not quite there

Answer 12

yes! Something along those lines

Answer 13

you'll use the rule

\[\Large b^x = y \ \ \implies \ \ \log_b(y) = x\]

Answer 14

Ok thank-you :)!!

Answer 15

what about the 8 pascals?

Answer 16

how would you use that rule to rewrite \[\Large 2^x = 8\]

Answer 17

Look at base b^x=y as if it were 2^x=8

Answer 18

Now look at the log equation and replace each variable with the corresponding one.

Answer 19

yeah so b = 2 and y = 8

Answer 20

That's it right?

Answer 21

what log equation do you have now

Answer 22

2^x = 8 means log(base 2) 8 = x

Answer 23

good

Answer 24

That's it then?

Answer 25

yeah \[\Large 2^x = 8\] turns into \[\Large \log_2(8) = x\]

Answer 26

Thank you so much~~!!

Answer 27

I have one more?

Answer 28

go ahead

Answer 29

what are your thoughts?

Answer 30

it's suppose to be 50^x. Sorry!

Answer 31

I would tell her to convert it. I dont know which formula to use now though

Answer 32

you'd use the one I just posted. The rule going from exponential to log

Answer 33

Ok. Lemme try it

Answer 34

log 50 (17)=x

Answer 35

yes, \[\Large \log_{50}(17) = x\]

Answer 36

That's it? It was that simple?

Answer 37

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

Answer 38

Thank you!!!

Answer 39

Can I ask one last question? Pleasee?

Answer 40

sure

Answer 41

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.

Answer 42

Ty!

Answer 43

it says `The graph of the two functions is below`

where do the two functions cross?

Answer 44

oh hold on! I can graph it

Answer 45

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIzXngiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjAsImVxIjoiLXgrNCIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MTAwMH1d

Answer 46

looks good

Answer 47

where do the two functions cross?

Answer 48

at (1,3)

Answer 49

what does that point mean?

Answer 50

It is the solution?

Answer 51

it's the solution to the system, yes

but what does that solution mean in terms of the word problem?

Answer 52

The number of people who leave the park early due to the temperature?

Answer 53

let's go back to each function one by one

f(x) = 3^x

what is x? what is f(x)?

Answer 54

umm the increase in temperature for f(x)?

Answer 55

for f(x) = 3^x

x = temperature
f(x) = number of visitors

Answer 56

how about g(x) = -x+4 ?

Answer 57

-x=temperature or people leaving?

Answer 58

x looks like the change in temp

Answer 59

yes

Answer 60

hmm..is that when the temperature and # of people are equal?

Answer 61

Wait! NVM haha

Answer 62

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

Answer 63

I know right? Ugh!!! So, would (1,3) mean that that's the temp. needed to have the most visitors?

Answer 64

maybe it's when the temp change is +1, then the number of visitors equals the number of people who leave early

Answer 65

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

Answer 66

Oh! I didn't look at it that way! That is strange.

Answer 67

It's a poorly worded question tbh

Answer 68

yeah I agree

Answer 69

i'm going to go with your answer :)

Answer 70

Thanks so much for all your help today!!! You're awesome :D

Answer 71

sure thing