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The function, f(x) = 6000/1+4000e^-0.6x, describes the number of students at a college...

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andrewmezzo | Student, College Freshman | Valedictorian

Posted May 2, 2013 at 1:16 PM via web

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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?

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violy | High School Teacher | (Level 3) Assistant Educator

Posted May 2, 2013 at 1:43 PM (Answer #1)

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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.

 

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