SOLUTION: A contagious disease is infecting residents of a town of 7,300 residents. The number of residents infected t days after the disease has begun is given by the function {{{f(t)=(

Algebra ->  Graphs -> SOLUTION: A contagious disease is infecting residents of a town of 7,300 residents. The number of residents infected t days after the disease has begun is given by the function {{{f(t)=(      Log On


   

Question 150022: A contagious disease is infecting residents of a town of 7,300 residents.
The number of residents infected t days after the disease has begun is given by the function f%28t%29=%287300%29%2F%281%2B500e%5E%28-0.5t%29%29

How many residents are infected with the disease after 6 days?




Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

f%28t%29=%287300%29%2F%281%2B500e%5E%28-0.5t%29%29 Start with the given equation.


f%286%29=%287300%29%2F%281%2B500e%5E%28-0.5%286%29%29%29 Plug in t=6.


f%286%29=%287300%29%2F%281%2B500e%5E%28-3%29%29 Multiply -0.5 and 6 to get -3


f%286%29=%287300%29%2F%281%2B500%280.04979%29%29 Raise "e" to the negative 3rd power to get 0.04979


f%286%29=%287300%29%2F%281%2B24.895%29 Multiply 500 and 0.04979 to get 24.895


f%286%29=%287300%29%2F%2825.895%29 Add 1 to 24.895 to get 25.895


f%286%29=281.9077 Divide

So rounding to the nearest whole number (since 0.9077 of a person doesn't make sense), we get 282 people.

So after 6 days, about 282 residents are infected.