Question

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?

Answer 1

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.