The function, f(x) = 6000/1+4000e^-0.6x, describes the number of students at a college with 6000 students who became ill with influenza x days after its initial outbreak. The cllege decides the suspend classes at the point were 60% of the students are ill. How many days after the influenza outbreak will this occur?
We know that the college decides the suspend classes at the point were 60% of the students are ill. So, we will first take the 60% of the number of students. So, we take the 60% of 6000.
60% of 6000 = 0.60 * 6000 = 3600.
We are asked to calculate how many days will 3600 students suffered an influenza.
We plug-in f(x) = 3600, and solve for x.
`3600 = 6000/(1 + 4000e^(-0.6x))`
First, multiply both sides by 1 + 4000e^(-0.6x).
`3600(1 + 4000e^(0.6x)) = 6000`
Divide both sides by 3600.
`1 + 4000e^(-0.6x) = 1.6666666667`
Subtract both sides by 1, and divide both sides by 4000.
`e^(-0.6x) = 0.000166666666675`
Take the natural logarithm of both sides.
`-0.6x = ln(0.000166666666675)`
Divide both sides by -0.6.
Therefore, it will take 14.45 or 14 days after the influenza outbreak will occur.