Answer
$f(t)=\displaystyle \frac{10,000}{1+9(1.25)^{-t}}$
$f(7)\approx 3463$ cases
Work Step by Step
Logistic Model form: $\displaystyle \quad f(t)=\frac{N}{1+Ab^{-t}}$
$N$ is the limiting value, the total population. $N=10,000$
Now (t=0 days), we are given
$f(0)=1000 \quad \Rightarrow \quad \left\{\begin{array}{ll}
1000 & =\dfrac{10000}{1+Ab^{-0}}\\
1+Ab^{-0} & =\dfrac{10000}{1000}\\
A & =10-1\\
A & =9
\end{array}\right.$
The rate of increase was $ 25\%$ per day, which corresponds to a factor $b=100\%+25\%=1.25$
$f(t)=\displaystyle \frac{10,000}{1+9(1.25)^{-t}}$
A week from now, $t=7$ days, we have:
$f(7)\approx 3463$ cases
