Find C and a so that f(x)= Ca^x Satisfies the given equations

Question

f(-2)=4/5

 

f(2)=1/20

Answer 1

Since f(-2) = 4/5, Ca^-2 = 4/5

 

Since f(2) = 1/20, Ca² = 1/20  

 

From the first equation, we have a² = 5C/4

 

Substituting into the other equation, we get C(5C/4) = 1/20

 

                                                                       C² = 1/25

 

                                                                       C = 1/5

 

 Since C = 1/5 and a² = 5C/4, we have a² = 1/4

 

                                                         a = 1/2

 

f(x) = (1/5)(1/2)^x