Exponential and Logarithmic Functions - Applications of Exponential and Logarithmic Functions

In a garden with \(10\,000\) plants, a disease begins spreading after one plant is infected by virus. Assuming all plants are susceptible to the disease, the number of plants \(N\) infected \(t\) days after the disease begins spreading is modelled by the equation \(N=\frac{10\,000}{1+9999{{\mathrm{e}}^{-0.2t}}}\).

1. Find the expected number of plants infected after \(7\) days.
2. Estimate the number of days required for one-quarter of the plants in the garden to become infected.