SOLUTION: Can someone please explain this to me? I have no idea where to even start! Much appreciated. Find an exponential function of the form f(t) = Y 0 bt to model the data. The num

Question 153144: Can someone please explain this to me? I have no idea where to even start! Much appreciated.

Find an exponential function of the form f(t) = Y 0 bt 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) = Y 0 bt
b) Estimate the number of cassettes sold in 2004.
c) When will the number of cassette sales drop below 1.5 million?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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
--------
17.2 = 272.6 b^8
b^8 = 0.063096...
b = 0.707946...
EQUATION:
f(t) = 272.6*0.707946^t
-----------------------------------
b) Estimate the number of cassettes sold in 2004.
f(9) = 272.6*0.707946^9 = 12.176677 million
--------------------------------------
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
==========================
Cheers,
Stan H.

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