SOLUTION: Working on this problem and don't know how to approach it - Use the given conditions and the table below to find C, a, and f(x) = Ca^x Given: f(1) = 18 and f(2) = 9 x | -1

Algebra ->  Exponents -> SOLUTION: Working on this problem and don't know how to approach it - Use the given conditions and the table below to find C, a, and f(x) = Ca^x Given: f(1) = 18 and f(2) = 9 x | -1       Log On


   

Question 248007: Working on this problem and don't know how to approach it -
Use the given conditions and the table below to find C, a, and f(x) = Ca^x
Given: f(1) = 18 and f(2) = 9
x | -1 | 0 | 1 | 2
---+----+----+----+----
y | | | |

Plugging in the givens I get this -
x | -1 | 0 | 1 | 2
---+----+----+----+----
y | | | 18 | 9

but don't know where to go from there.
Thanks for your help - Ryan

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+Ca%5Ex Start with the given equation.


18+=+Ca%5E1 Plug in f%28x%29=18 and x=1


18+=+Ca Simplify


18%2Fa+=+C Divide both sides by 18.


So C=18%2Fa


---------------------------


f%28x%29+=+Ca%5Ex Go back to the given equation.


9+=+Ca%5E2 Plug in f%28x%29=9 and x=2


9+=+%2818%2Fa%29a%5E2 Plug in C=18%2Fa


9+=+%2818a%5E2%29%2Fa Multiply


9+=+18a Reduce


9%2F18+=+a Divide both sides by 18.


1%2F2=a Reduce.


So a=1%2F2. So the value of C is C=18%2Fa=18%2F%281%2F2%29=18%282%2F1%29=36 giving us the function f%28x%29=36%281%2F2%29%5Ex