Town has popultion of 5,000.Number of people infected after t days with a disease is

N(t) = 5000/1 + 21.7e^-0.4t

Find number initially infected
find number infected after 12 days

To find the number initially infected, we need to determine the value of N(t) when t = 0.

The equation N(t) = 5000 / (1 + 21.7e^(-0.4t)) calculates the number of people infected after t days.

When t = 0, the equation becomes N(0) = 5000 / (1 + 21.7e^(-0.4 * 0)).

Since anything raised to the power of 0 is 1, the equation simplifies to N(0) = 5000 / (1 + 21.7e^(0)).

Since e^(0) is equal to 1, the equation further simplifies to N(0) = 5000 / (1 + 21.7).

To find the number initially infected, we need to calculate N(0) based on this simplified equation.

N(0) = 5000 / (1 + 21.7)

Now, let's evaluate this expression.

N(0) = 5000 / 22.7

Performing the division, we find the number initially infected:

N(0) ≈ 220.26 (rounded to two decimal places)

Therefore, approximately 220.26 people were initially infected.

Now, let's find the number of people infected after 12 days.

We plug in t = 12 into the equation N(t) = 5000 / (1 + 21.7e^(-0.4t)):

N(12) = 5000 / (1 + 21.7e^(-0.4 * 12))

Simplifying this equation yields:

N(12) = 5000 / (1 + 21.7e^(-4.8))

Now, let's evaluate this expression.