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

Find C and a so that f(x) = Ca^x satisfies the given conditions.
 
f(1) = 25, f(2) = 125
 
a = ?

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Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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   √

Comments

Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
1
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
 
 
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
0
 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