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

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3 Answers

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   √

Comments

Comment

Hi Keith;
f(x)=cax
f(1)=ca1=25=52
c=5
a=5
f(2)=ca2=125
f(2)=(5)(52)=(5)(25)=125
 
 
 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