Question

The function N(t)= 6000/1+999e⁻ᵗ models the number of people in a small town who have caught the flu t weeks after the initial outbreak.

How many people have caught the flu after 2 weeks?

Answer 1

To calculate the number of people who have the flu after 2 weeks, we substitute t=2 in the given function N(t) = 6000/(1+999e^-t). After simplification, we find that approximately 44 people have caught the flu after 2 weeks.

Step-by-step explanation:

The student has asked to determine the number of people in a small town who have caught the flu after 2 weeks based on the function N(t) = 6000/(1+999e-t), where t is the time in weeks after the initial outbreak. To find out how many people have the flu after 2 weeks, we substitute t = 2 into the equation:

N(2) = 6000/(1+999e-2)

First, we calculate the exponent part:

e-2 ≈ 0.1353

Now, replace this value back into the equation:

N(2) = 6000/(1+999 * 0.1353)

This simplifies to:

N(2) = 6000/(1+135.1647)

N(2) = 6000/136.1647

N(2) ≈ 44.06

Therefore, approximately 44 people have caught the flu after 2 weeks.