Algebra Question

Question

Find C and a so that f(x)=Ca^x satisfies the given equation.

Find C and a so that f(x)=Ca^x satisfies the given equation.

 

f(-2) = 25/4,   f(2) = 1/100

      

 

a = ?

C=?

Answer 1

f(-2) = 25/4

25/4 = C*a^(-2)

(25/4)*a^2 = C

a^2 = (4c)/25 <--- please label this

equation ALPHA

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f(2) = 1/100

1/100 = C*(a^2)

1 = 100*C*a^2

1 = 100*C * (4c)/25

25 = 400 * c^2

(25/400) = c^2

1/16 = c^2

c = 1/4

then a^2 = 1/25

a = 1/5

the function is f(x) (1/4)* (1/5)^x