Answer:
Noting that e^b = 6/a
Explanation:
Use the general expo function y = ae^(bx).
Subbing 6 for y and 1 for x, we get 6 = ae^(b), or e^b = 6/a.
Subbing 12 for y and 2 for x, we get 12 = ae^(2b), or 12/a = (e^b)²
Now let's find the value of the coefficient a. Noting that e^b = 6/a, rewrite
12/a = (e^b)² as 12/a = (6/a)².
Dividing both sides by 6/a, we get 2 = 6/a, or a = 3.
Again Noting that e^b = 6/a, e^b = 6/3, or e^b = 2.
Taking the natural log of both sides, we get b = ln 2.
Then our y = ae^(bx) becomes:
y = 3e^(ln 2·x), or y = 3·2^x
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