# 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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