The flu is spreading to 25 students per day. To find dP/dt, we need to invoke the Chain Rule twice: At t = 3, then, dP/dt = 100 / 4 = 25. To find the rate at which the flu spreads, we find dP/dt.P(0) = 100 / (1 + e3 ) = 5 students to the nearest whole number.The graph of P as a function of t is shown in Figure 3.58.When will the flu spread at its maximum rate? What is this rate?.How fast is the flu spreading after 3 days?.Estimate the initial number of students infected with the flu.Many of them may already be well again at time t. The spread of a flu in a certain school is modeled by the equationwhere P(t) is the total number of students infected t days after the flu was first noticed.Setting these two formulas for m equal to each other, we have:.The tangent line there has slope m = 1 / a since the tangent line passes through the origin, its slope is:.
It has coordinates (a, ln a) for some positive a, and.However, we do know two important facts about that point:.This problem is a little more difficult than it looks, since we do not know the point of tangency.A line with slope m passes through the origin and is tangent to the graph of y = ln x.At what point on the graph of the function y = 2t – 3 does the tangent line have slope 21?.3.9 Derivatives of Exponential and Logarithmic Functions
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