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^-0.5 t
How many residents are infected with the disease after 6 days?
When you transcribe formulae involving fractions written in full to a single line, please do not forget that numerators and denominators have implicit parentheses around them.
As an example, instead of writing 7300/1+t, it should be written as 7300/(1+t).
I suspect the same applies to the above equation. I interpret it as
f(t):=7300/(1+500*e^(-0.5)*t)
If you follow the correct priority of operations (using your original equation), you should arrive at
f(6) = 281.92 = 282 persons.
The order of operations calls for calculating -0.5t first, then do the exponentiation in the denominator, multiply by 500 and add to 1.
Finally, divide 7300 by the resulting number in the denominator.
Remember, a badly transcribed formula gives equally bad results.
To find the number of residents infected with the disease after 6 days, we need to evaluate the function f(t) at t = 6.
Substituting t = 6 into the function:
f(6) = (7300)/(1 + 500e^(-0.5*6))
Now, let's simplify the expression:
f(6) = (7300)/(1 + 500e^(-3))
Using a calculator, we can calculate the value of e^(-3) and substitute it into the equation:
f(6) ≈ (7300)/(1 + 500 * 0.0498)
f(6) ≈ (7300)/(1 + 24.9)
f(6) ≈ (7300)/(25.9)
Using a calculator, we can evaluate this expression:
f(6) ≈ 281.85
Therefore, approximately 282 residents are infected with the disease after 6 days.