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19 March, 12:19

A particular country's exports of goods are increasing exponentially. The value of the exports, t years after 2007 , can be approximated by V (t) equals1.5 e Superscript 0.039 t where tequals0 corresponds to 2007 and V is in billions of dollars. a) Estimate the value of the country's exports in 2007 and 2012. b) What is the doubling time for the value of the country's exports?

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  1. 19 March, 12:37
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    V (t) = $ 1.5 billion for 2007

    V (t) = $1.5 billion, 295 million. For 2012

    Doubling time = t = 177.69 yrs

    Explanation:

    a).

    V (t) = 1.5e^ (0.039t)

    For the first year 2007, t = 0

    V (t) = 1.5e^ (0.039*0)

    V (t). = 1.5e^0

    V (t) =. 1.5*1 = 1.5

    V (t) = $ 1.5 billion for 2007

    For 2012 that is 5 years after, t = 5

    V (t) = 1.5e^ (0.0039*5)

    V (t) = 1.5e^ (0.0195)

    V (t) = 1.5 (1.019691367)

    V (t) = 1.5295

    V (t) = $1.5 billion, 295 million.

    b). Doubling time is when the value of the export is 1.5 * 2 = $ 3 billion

    3 = 1.5e^ (0.0039t)

    3/1.5 = e^ (0.0039t)

    2 = e^0.0039t

    In 2 = 0.0039t

    0.693 = 0.0039t

    t = 177.69 yrs
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