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.