Wendy is looking over some data regarding the strength of some rope and how that relates to its number of woven strands. The data seems to be exponential. How can Wendy determine if the data is exponential and how can she convert it to a log function?

Can anyone help walk me through this one?

Question

Wendy is looking over some data regarding the strength of some rope and how that relates to its number of woven strands. The data seems to be exponential. How can Wendy determine if the data is exponential and how can she convert it to a log function? 

Can anyone help walk me through this one?

anonymous · Answer

@amistre64

anonymous · Answer

@campbell_st @dan815 @eliassaab @FlvsGirl @Gravity_Dreams @Hero

anonymous · Answer

Can you help @Gravity_Dreams  ?

anonymous · Answer

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anonymous · Answer

So far I found that to be exponential, the stronger rope is the more threads there are. And then that's about it.

anonymous · Answer

@johnweldon1993 @yolo_swag_lyfe @Koikkara @Luigi0210 @mathmale

anonymous · Answer

well i dont have a clue bro sorry :(

anonymous · Answer

thanks anyway

amistre64 · Answer

found it :)

amistre64 · Answer

what are all the ways an exponential graph can take?

anonymous · Answer

hmm. im not sure

amistre64 · Answer

well, theres the baisc function:$$y=b^x$$
we can scale it, move it along the x axis, and move it along the y axis

anonymous · Answer

ok

amistre64 · Answer

$$y=ab^{x-h}+k$$

amistre64 · Answer

since only x and y are known .. we would need at least 4 points to determine the 4 unknowns to model something with

anonymous · Answer

so these can be random points?

amistre64 · Answer

well, no.  they would be taken from the specific data that was gathered ... which is not presented in the problem as posted.

anonymous · Answer

right. So how do you get those points with what we do have?

amistre64 · Answer

we have no data presented to us so we cant formulate a specific function as is.

amistre64 · Answer

the question is asking for a method to determine IF the data is exponential.  this is the method i would use ... among a few other ideas

amistre64 · Answer

if the data is 'roughly' exponential, then we can develop an exponential regression line, but if your class is not in statisitics then its prolly not the way they expect you to go about it

anonymous · Answer

no we aren't in stat right now- just log functions

amistre64 · Answer

then i would stick with my first thought :)

amistre64 · Answer

spose we had 4 points we could fill in:$$y_1=ab^{x_1-h}+k\
y_2=ab^{x_2-h}+k\
y_3=ab^{x_3-h}+k\
y_4=ab^{x_4-h}+k
$$
we have 4 equations and 4 unknowns, substitution might help to work out way thru it to determine the unknowns.  but withoutany specific data this is the best shot we have as an explanation .

amistre64 · Answer

given that, take the general setup and invert it ....,  solve for 'x' in terms of 'y'

anonymous · Answer

okay.  but someone in a different equation had a specific equation and just put it into a log function. Is that an easier way?

anonymous · Answer

@amistre64

anonymous · Answer

@AnonymousBeast

anonymous · Answer

If you look at the data, you can tell by multiplying a y value to get to the next by a certain number. 
$$y=b^x \rightarrow \log_{b} y=x$$

anonymous · Answer

I'm sorry, I recently joined and haven't read the above text. The answer to what exactly? The original question? If so, If Wendy observes the data and sees that output values are each multiplied by a certain number to get the next, then the data is exponential. She can convert the exponential function into a logarithmic function using the formula I showed you above.

anonymous · Answer

okay- that must be how it is since in the problem it says it is an exponential function

anonymous · Answer

Alright, very well. Is that all?

anonymous · Answer

yes thank you!

anonymous · Answer

You're welcome.