SOLUTION: I think this question requires logarithms Given the equation y=a*b^x find the values of a and b for the curve that passes through the points (-2, 1) and (2,5) Sorry if it's t

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I think this question requires logarithms Given the equation y=a*b^x find the values of a and b for the curve that passes through the points (-2, 1) and (2,5) Sorry if it's t      Log On


   

Question 992730: I think this question requires logarithms
Given the equation y=a*b^x find the values of a and b for the curve that passes through the points (-2, 1) and (2,5)
Sorry if it's the wrong section, but I don't really know what to do.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Your model in general y=ab%5Ex is useful also for the logarithms of its left and right side
members.
Choose either base 10 or e. Here will be using base 10.

log%2810%2Cy%29=log%2810%2C%28ab%5Ex%29%29
log%2810%2Cy%29=log%2810%2Ca%29%2Bx%2Alog%2810%2Cb%29
highlight_green%28log%2810%2Cy%29=x%2Alog%2810%2Cb%29%2Blog%2810%2Ca%29%29

You now want to adjust your given points to use log%2810%2Cy%29 instead of the y coordinates as given
because that is how the equation has been treated. Your points to use in the green-outlined equation
must now be (-2, log(10,1)) and (2, log(10,5)).
Those points, if decimal form will help, (-2,0) and (2,0.6990).
-
Again, these points are for the LINEAR equation outlined in green - NOT for the original model
of y=ab%5Ex.

Now you have the two points, treated for their logarithms of y, and you can find the
vertical axis intercept which is log%2810%2Ca%29 and the slope which is log%2810%2Cb%29.
That allows you to find a and b.