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)= 7300/1+500e-0.5t
How many residents are infected with the disease after 6 days?
Maybe you mean
f = 7300/ (1+500e^-.5t ) ????
at t = 0 then
f = 7300/ (501) = 14.67
at t = 6
f = 7300 / (1 + 500*.05) = 282
I didn't think 0.5t was suppose to be treated as a square root; probably why I was having difficulty. Thanks
To find out how many residents are infected with the disease after 6 days, we need to substitute the value of t = 6 into the function f(t) = 7300 / (1 + 500e^(-0.5t)).
Let's start by plugging in t = 6 into the equation:
f(6) = 7300 / (1 + 500e^(-0.5*6))
Now, we can simplify the calculation step by step:
f(6) = 7300 / (1 + 500e^(-3))
f(6) = 7300 / (1 + 500 * 0.04978706836) (using e^-3 = 0.04978706836)
Next, we can calculate the value inside the brackets:
f(6) = 7300 / (1 + 24.89353418)
f(6) = 7300 / 25.89353418
Finally, we can divide 7300 by 25.89353418 to find the number of residents infected after 6 days:
f(6) ≈ 281.8922166
Therefore, approximately 282 residents are infected with the disease after 6 days.