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Unformatted text preview: e: talk to your science faculty. 6.5 Applications of Exponential and Logarithmic Functions 389 This is all well and good, but the quadratic model appears to ﬁt the data better, and we’ve yet to
mention any scientiﬁc principle which would lead us to believe the actual spread of the ﬂu follows
any kind of power function at all. If we are to attack this data from a scientiﬁc perspective, it does
seem to make sense that, at least in the early stages of the outbreak, the more people who have
the ﬂu, the faster it will spread, which leads us to proposing an uninhibited growth model. If we
assume N = BeAt then, taking logs as before, we get ln(N ) = At + ln(B ). If we set X = t and
Y = ln(N ), then, once again, we get Y = AX + ln(B ), a line with slope A and Y -intercept ln(B ).
Plotting ln(N ) versus t and gives the following linear regression. We see the slope is a ≈ 0.202 and which corresponds to A in our model, and the y -intercept is
b ≈ 5.596 which corresponds to ln(B ). We get B ≈ 269.414, so that our model is N = 269.414e0.202t .
Of course, the calculator has a built-in ‘Exponential Regression’ feature which produces...
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