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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   √

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