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Can anyone help me with this math problem?

DVD Videos. The total number of DVD videos produced and shipped in 1998 was 0.5 million. In 2004, the total number of units reached 29.01 million. 

Assuming the exponential model applies:

a) find the value of k and write the function

b) Estimate the number of DVD videos produced and shipped in 2005, in 2008, and in 2011. 

I attached the graph model!

Attachment image

1 Answer

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  • 1 month ago

    Being an exponential model it will have the form of 

    N(t) = Ae^(kt)

    When t = 0 (1998)

    N(0) = 0.5e^(k(0)) => 

    N(0) = 0.5e^(0) => 

    N(0) = 0.5(1) = 0.5 

    Hence A = 0.5 

    When N(6)  = 2004 

    N(6) = 29.01 = 0.5e^(6k)

    29.01/0.5 = e^(6k)

    58.02 = e^(6k)

    Take natural logs (ln) 

    ln(58.02) = 6k    (NB lne= 1)

    4.06078 = 6k 

    k = 4.06078 / 6 

    k = 0.67679

    Hence the eq'n becomes 

    N(t) = 0.5e^(0.67679t)

    In 2005 t = 7 

    N(7) = 0.5e^(0.67679(7)) 

    N(7) = 0.5e^(4.73753) 

    N(7) = 0.5(114.1518

    N(7) = 57.07 million  (in 2005)

    In 2008 ; t = 10 

    N(10) = 0.5e^(0.67679(10))

    N(10) = 0.5 e^(6.7679)

    N(10) = 0.5(869.48)

    N(10) = 434.74 million ( in 2008)

    Similarly in 2011 ; t = 13

    N(13) = 0.5e^(0.67679(13)) 

    N(13) = 0.5(e^(8.79827)

    N(13) =0.5( 6622.776)

    N(13) = 3311.38 million.  ( or 3.311 billion). 

    hope that helps!!!!

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