In the image below from this video lesson, the teacher shows how to get an exponential function from a pattern of data, also copied below. You can see that her solution using the formula (a)(b) to the power of x is f(x) = 4(3) to the power of x. She explains that she is multiplying 4 by 3 because the values in the y column increase by 3, but she doesn't explain why she is using 4 for the a value?

Question: for the set of data below, if the b value of (a)(b) to the power of x is 3, why is the a value 4?

x   y
-1   4/3
0   4
1   12
2   36
3  108

enter image description here


If you know, that the data are the result of an exponential function, then you take two data points and write down two equations. The general function is $f(x)=a\ \cdot b^x$. For example you can take the first two data points $(-1/\frac{4}{3})$ and $(0/4)$. Now you can insert the values in the equation:

$a\cdot b^{-1}=\frac{4}{3}$

$a\cdot b^{0}=4$

Solve this little equation system for a and b. By looking at the second equation it can be easily evaluated, that $a=4$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.