SOLUTION: In class we learned a lesson on exponential functions, and all the problems we did solved out very easily and evenly. However this paper my teacher gave me has questions that are n

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: In class we learned a lesson on exponential functions, and all the problems we did solved out very easily and evenly. However this paper my teacher gave me has questions that are n      Log On


   

Question 931516: In class we learned a lesson on exponential functions, and all the problems we did solved out very easily and evenly. However this paper my teacher gave me has questions that are not as simple as the ones we learned i class, and I have no idea what to do for the last steps.
Problem:
Write an exponential function of the form y=ab^x whose graph passes through the given points.
1. (1,4), (2,12)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Find logarithms of both sides of the equation form.

ln%28y%29=ln%28ab%5Ex%29, choosing base e just for convenience.
ln%28y%29=ln%28a%29%2Bln%28b%5Ex%29
ln%28y%29=ln%28a%29%2Bx%2Aln%28b%29
highlight_green%28ln%28y%29=x%2Aln%28b%29%2Bln%28a%29%29

That is a linear equation with slope ln(b) and vertical axis intercept ln(a).

Treat your given points properly.
The point given (1,4) must be converted into (1,ln(4)).
The other point given (2,12) must be used as (2,ln(12)).
The slope will be ln%28b%29=%28ln%2812%29-ln%284%29%29%2F%282-1%29. Find the value for b using this slope information.

How to find ln(a):
Solve the linear form for ln(a) and then choose either of the converted points.
ln%28a%29=ln%28y%29-x%2Aln%28b%29, and you would know ln(b) from the previous calculations....
Find the value for a.