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

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

a = ?

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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Westford, MA

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 √

Middletown, CT

Hi Keith;

f(x)=ca^{x}

f(1)=ca^{1}=25=5^{2}

c=5

a=5

f(2)=ca^{2}=125

f(2)=(5)(5^{2})=(5)(25)=125

Woodland Hills, CA

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

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