Find the exponential function

[Bonafide]

Homework Statement

Find the exponential function that passes through the points (2, 1) and (5, 7).

Homework Equations

y= Ce^ (kt)

The Attempt at a Solution

I can only get as far as substituting in 2 for t and 1 for y, then I'm completely stuck.

 

[Bacat]

There is a good tutorial for how to do this: http://wcherry.math.unt.edu/math1650/exponential.pdf"

Look at the bottom of page 3 and then the example that starts at the bottom of page 9.

Using this method, I find the answer to be:

[tex]k=\frac{ln7}{3}[/tex]


[tex]c=7^{-2/3}[/tex]

 

[Bonafide]

Thanks for the help bacat!

 

[Dick]

There is a good tutorial for how to do this: http://wcherry.math.unt.edu/math1650/exponential.pdf"

Look at the bottom of page 3 and then the example that starts at the bottom of page 9.

Using this method, I find the answer to be:

[tex]k=\frac{ln7}{3}[/tex][tex]c=7^{-2/3}[/tex]

Um. Bacat, giving an explicit worked out answer violates the Forum rules.

 

[Bacat]

Hi Dick,

I certainly didn't intend to violate any forum rules, though I disagree that I gave an explicitly worked out answer. I provided a link to a tutorial that has a derivation of the solution in general with an included example. The astute mathematics student must still decide how it applies to his homework problem and plug in the appropriate values to find the answer. This approach to teaching mathematics is commonly found in textbooks- a derivation of the solution and an example. This is followed by exercises that the student must work out on their own.

While it's true that I gave an answer, I did not explicitly work it out for him. I gave the answer as a means of checking his work. This is not unlike the answers to odd-numbered questions in the back of a mathematics textbook. The average instructor would not give full credit for simply writing down the formula from the link and the answer I posted, unless he had derived the formula in class already. But even then he would expect to see how the student plugged in the points to arrive at the answer.

If the question had been to derive the solution to this type of problem, my approach would have certainly been wrong. But the question was an exercise. In providing a link to the derivation, I meant to support whatever teaching of this material the instructor has already done. I'm certain that the instructor taught the students how to solve this type of problem in class at some point. Perhaps Bonafide was absent, or wasn't paying attention, or didn't understand because the instructor did not cover the material carefully. He still must read and understand the derivation on his own if he is to understand the material and perform well on the exam.

Perhaps your intention is to ask me not to provide answers for people to check their work? That seems reasonable if that is the policy.

 

[Dick]

Hi Bacat,

I think providing the solution is a disincentive for the student to carefully work through the provided examples. It is true you didn't give the full solution, and that's what the Forum rules prohibit. I think it's better just to give them a hint to get them to the next step. The main reason I chimed in was that I thought your solution was wrong because I made a mistake. But everybody has to make their own judgement call as to how much is 'too much'. What you did is probably not 'too much'. Now I'm wondering if I just left the rest of the message standing because I was feeling crabby. Sorry to be such a nit.

Dick

 

[Bacat]

No worries, Dick.

I appreciate your effort to make these forums beneficial for people seeking help. I also use them for homework and I find them tremendously valuable. That's the main reason I try to give back.

I'll avoid giving answers in the future. I think your point of view is based on solid experience.

Cheers!

 

[Dick]

Ditto Bacat. Thanks for helping. Cheers from here!