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

Question

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

 

f(1) = 25, f(2) = 125

 

a = ?

Answer 1

f(x) = C a^x

 

f(1) = 25 = C a => C = 25/a

 

f(2) = 125 = C a^2 = (25/a)*a^2 = 25 a^(2-1)

 

125/25 = a^1

 

a = 5

 

C = 25/5 = 5

 

f(x) = 5*5^x = 5^(x+1) ; which is y = 5^x shifted left 1.

 

check:

 

f(1) = 5^(1+1) =? 25

 

5^(2) = 25   √

 

f(2) = 5^(2+1) =? 125

 

5^(3) = 125   √

Answer 2

Hi Keith;

f(x)=ca^x

f(1)=ca¹=25=5²

c=5

a=5

f(2)=ca²=125

f(2)=(5)(5²)=(5)(25)=125

 

 

Answer 3

 f( x ) = C a ^ X

 

f ( 1) = C (a^ 1) = 25

 

f ( 2 ) = C ( a ^2 ) = 125

 

  f( 2) / f( 1) = C ( a^2) / C ( a ^1) = a =  125 / 5 = 25