Question 153144
Find an exponential function of the form f(t) = Yo b^t to model the data. The number of music cassette tapes sold in 1995 was 272.6 million and in 2003 the number sold was 17.2 million. Let x = 0 in 1995. 
a) Build a model of the form f(t) = Yo b^t
272.6 = Yo b^0
Therefore Yo = 272.6 million
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17.2 = 272.6 b^8
b^8 = 0.063096...
b = 0.707946...
EQUATION:
f(t) = 272.6*0.707946^t
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b) Estimate the number of cassettes sold in 2004.
f(9) = 272.6*0.707946^9 = 12.176677 million
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c) When will the number of cassette sales drop below 1.5 million?
272.6*0.707946^t < 1.5
0.707946^t < 0.005503
t*ln(0.707946)< ln(0.00550)
t < ln(0.0055)/ln(0.707946)
t < -5.202540/-0.345387
t < 15.06
Ans: 1995 + 15 = 2010
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Cheers,
Stan H.