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## Homework Statement

Students at Bacteria University begin showing flu-like symptoms. On the first day of term, 5 students have the flu. The growth of the number of infected students is modeled by

P(t) = 5e

^{0.3t}

What is a formula for the rate of change of the number of infected students in terms of t?

To the nearest whole number, what is the rate of change in the number of infected students when t=10 days?

## Homework Equations

f(x) = x

^{n}

f'(x) = nx

^{n-1}

## The Attempt at a Solution

P(t) = 5e

^{0.3t}

P'(t) = (5t*e)

^{-0.3t}

P'(10) = 50e

^{-3}

P'(10) = 1/50e

^{3}

Now I know that this deceleration is not right since the infection rate only starts decelerating when half of the population has been infected and it is very unlikely that half the population will be infected in 10 days.

However algebraically this makes sense since if you have a decimal exponent and you take the derivative you get a negative exponent in the derivative or in other words a fractional rate.