There were 15.37 million licensed drivers in Texas in 2009 and 14.54 million in 2004. Find a formula for the number, N, of licensed drivers in the US as a function of t, the number of years since 2004, assuming growth is
(a) Linear
N(t)= million drivers

(b) Exponential
N(t)= million drivers

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  1. N(t)=14.54+slope*Y

    Y = year-2009
    slope= (15.37-14.54)/5

    b. N(t)=14.54 e^(kY)
    y= year-2009
    k= 1/5 * ln(15.37/14.54)

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  2. If we consider 2004 to be represented by 0,
    then 2009 would correspond with 5
    and we have two ordered pairs (0,14.54) and (5,15.37)
    slope = (15.37-14.54)/(5-0) = .83

    N = .83t + c
    at (0,14.54)
    14.54 = 0 + c , c = 14.54

    N = .83t + 14.54 , where t is in years since 2004 and N is in millions of drivers

    You don't specify what type of exponential, (what base), so I will use base e

    N = a e^kt, were a is the initial number and t is the time since 2004
    N = 14.54 e^kt
    when t = 5
    15.37=14.54 e^(5k)
    1.057... = e^5k
    using ln
    5k = ln 1.057..
    k = .0111028.. or appr .0111

    N(t) = 14.54 e^(.0111 t)

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