You are here:

Calculus/Exponential Regression.

Advertisement

Expert: - 8/6/2009


Question
Hi, thanks a lot for helping me out.

Basically I have one question, its to assume that the graph of the exponential function, f(x)=ka^x passes through the points, fine the value of a and k.

The points are (1,1.5) and (-1,6)

Thanks.

Answer
Well, those are the values for x and f(x), so lets put them in.
We get 1.5 = k(a^1) and 6 = k(a^-1).

Since a^1 = a and a^-1 = 1/a, we have 1.5 = ka and 6 = k/a.

Now k can be solved for using both of the equations.
They gives us k = 1.5/a and k = 6a.

Using these two equations, since they are both solutions for k, we can equate them and get
1.5/a = 6a.  That is equivalant to 1.5/6 = a².

Now 1.5/6 can be multiplied by 2/2, giving 3/12, and that can be seen to be 1/4.
So what we have is 1/4 = a², which says that a = ±½.

Putting this back into both equations (only 1 is necessary, but this makes sure that what we got for a is correct) gives k = 1.5/±½ and k = 6(±½).

For the first solution, dividing by ½ is the same as multiplying by 2, so this says k = ±3.
Multiplying 6 by ±½ gives us ±3.  What do you know ... they both agree.

This says that the answer for (a, k) could be (½, 3) or (-½, -3) since the sign of one determines the sign of the other.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2012 About.com, a part of The New York Times Company. All rights reserved.