SOLUTION: rite an exponential function of the form y = ab^x whose graph passes thru the given points. (1,7), (2,49)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: rite an exponential function of the form y = ab^x whose graph passes thru the given points. (1,7), (2,49)      Log On


   

Question 399595: rite an exponential function of the form y = ab^x whose graph passes thru the given points. (1,7), (2,49)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+ab%5Ex
If the graph passes through the two given points then the coordinates of those points should fit the equation. So
%287%29+=+ab%5E%28%281%29%29+=+ab
and
%2849%29+=+ab%5E%28%282%29%29+=+ab%5E2
We now have two equations with two unknowns, a and b. We should be able to solve this system and find out what a and b are.

We can use the Substitution method. Solving the first equation for a we get:
7%2Fb+=+a
Substituting this into the second equation we get:
49+=+%287%2Fb%29b%5E2
which simplifies as follows:
49+=+%287%2Fb%29%28b%5E2%2F1%29
49+=+7b%5E2%2Fb
49 = 7b
Dividing by 7 we get:
7 = b
Using 7%2Fb+=+a and the value we just found for b, we can find a:
7%2F%287%29+=+a
1 = a
So a = 1 and b = 7. This makes the desired equation:
y+=+%281%29%2A%287%29%5Ex
or
y+=+7%5Ex