Question

A virus has infected 400 people in the town and is spreading to 25% more people each day. Write an exponential function to model this situation, then find the number of people that will be infected in 10 days. Is this growth or decay?

Answer 1

We have been given that a virus has infected 400 people in the town and is spreading to 25% more people each day. We are asked to write an exponential function to model this situation.

Since the number of infected people is increasing, so our model will be exponential growth model.

An exponential growth function is in form $y=a(1+r)^x$, where,

y = Final amount,

a = Initial amount,

r = Growth rate in decimal form,

x = Time.

Let us convert 25% into decimal form.

$25\%=\frac{25}{100}=0.25$

The initial number of infected people is $400$, so our function would be $y=400(1+0.25)^x$.

$y=400(1.25)^x$

To find the number of infected in 10 days, we will substitute $x=10$ in our given formula as:

$y=400(1.25)^{10}$

$y=400(9.3132257461547852)$

$y=3725.290298\approx 3725$

Therefore, there will be approximately 3725 infected people in 10 days.