How to find the exponential function y=ca^x, with points (1,2) and (2,1)

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

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

This value of 'a' leads to

c = 2/a

c = 2/0.5

c = 4

Since a = 0.5 and c = 4, the answer is y = 4*0.5^x

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step-by-step explanation: