Answer: y = 4*0.5^x
Explanation:
First we'll use the point (1,2) to help isolate c in terms of 'a'
y = c*a^x
2 = c*a^1 ... plug in (x,y) = (1,2)
2 = c*a
c = 2/a
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The use the last equation mentioned above, along with the second point (2,1) to help determine the value of 'a'
y = c*a^x
y = (2/a)*a^x .... replace c with 2/a
y = 2*a^(-1)*a^x
y = 2a^(-1+x)
1 = 2a^(-1+2) ... plug in (x,y) = (2,1)
1 = 2a^1
1 = 2a
a = 1/2 = 0.5
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This value of 'a' leads to
c = 2/a
c = 2/0.5
c = 4
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Since a = 0.5 and c = 4, the answer is y = 4*0.5^x
