pre-cal

I have 2 sets of coordinates (1, 410) and (12, 788) and need to calculate the rate of change over time using y=ae^bt. Since I don't have a coordinate at 0, I can't figure out how to calculate my starting value, or a, to solve this.

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  1. y=ae^bt
    a) 410=ae^(b*1)
    b) 788=ae^(12b)

    divide equation a) by b)

    410/788=e(b-12b)
    take ln of each side
    -11b=ln(420/788)
    b= .057
    Now , solve for a.
    410=ae^(.057*1)
    a= 410/1.0587=387
    y= 387e^(.057t)

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