Vidhyamath Forum

Integration

Rita Lamichhane

Student

A flu epidemic hits a town. Let $P (t)$ be the number of persons sick with flu at time $t$ , where time is measured in days from the beginning of the epidemic and $P (0) = 100$ . Suppose that after $t$ days the flu is spreading at the rate of $120 t - 3 t^{3}$ people per day. Find the formula for $P (t)$ .

10 Feb, 2025

Replies (1)

Vidhyamath Online

Instructor

Solution:

$P (t) = \int (120 t - 3 t^{3}) d t = 60 t^{2} - \frac{3}{4} t^{4} + C$

Given $P (0) = 100$ :

$100 = 60 \times 0 - \frac{3}{4} \times 0 + C \Rightarrow C = 100$

Thus, the formula is:

$P (t) = 60 t^{2} - \frac{3}{4} t^{4} + 100$

10 Feb, 2025

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