SOLUTION: In 1996, an outbreak of a disease infected 14 people in a large community. By 1997, the number of those infected had grown to 40. Find an exponential growth funtion that fits the

Question 302662: In 1996, an outbreak of a disease infected 14 people in a large community. By 1997, the number of those infected had grown to 40. Find an exponential growth funtion that fits the datta. Round decimals to 3 places.
Thank you,
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In 1996, an outbreak of a disease infected 14 people in a large community. By 1997, the number of those infected had grown to 40. Find an exponential growth funtion that fits the data. Round decimals to 3 places.
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Form: y = ab^x
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Solve for a and b.
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Points from narrative: (0,14),(1,40)
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Equations:
40 = ab^1
14 = ab^0
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From the 2nd equation: a = 14
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Divide 1st Eq. by 2nd to get:
b = 40/14 = 20/7
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Equation:
y = 14(20/7)^x where "x" is the number of years after 1996
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Cheers,
Stan H.
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