SOLUTION: here were 23.7 million licensed drivers in California in 2009 and 22.76 million in 2004. Find a formula for the number, N, of licensed drivers in the US as a function of t, the num

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: here were 23.7 million licensed drivers in California in 2009 and 22.76 million in 2004. Find a formula for the number, N, of licensed drivers in the US as a function of t, the num      Log On


   

Question 873581: here were 23.7 million licensed drivers in California in 2009 and 22.76 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
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
You can begin with a general rule N=Ie%5E%28kt%29 , N is the amount after time t, I is the initial amount at time 0.

You want to find a value for k.
Year 2004 will be t=0 and I=22.76 million.
Year 2009 will be t=5 and N=23.7 million.

Finding logarithms of both sides of the equation allows to create a linear form of the equation.
ln%28N%29=ln%28I%29%2Bkt
ln%28N%29=kt%2Bln%28I%29---linear equation, independant variable t, slope k, y-intercept ln(I).

First point:
ln%2822.76%29=k%2A0%2Bln%2822.76%29
but this tells nothing.

Second Point:
ln%2823.7%29=k%2A5%2Bln%2822.76%29
k%2A5=ln%2823.7%2F22.76%29
highlight_green%28k=%281%2F5%29ln%2823.7%2F22.76%29%29. Simply need compute this k value.
highlight%28k=0.00809%29.
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Now the rule is more specific.
highlight%28highlight%28N=22.76%2Ae%5E%280.00809t%29%29%29.