Exponential and Logarithmic Functions - Applications of Exponential and Logarithmic Functions

The population model is an approximation: at \(t=0\), it gives \(1640/2900\approx0.566\), which rounds to one animal. Keep the supplied model constants.

On a farm with \(1640\) animals, one animal was infected with a contagious disease. The spread of the disease among the animals is modelled by the equation \(N=\frac{1640}{1+2899{{\mathrm{e}}^{-0.65t}}}\), where \(N\) is the total number of infected animals after \(t\) days. The farm management plans to quarantine the animals for a week if more than \(40\%\) of the animals are infected. Estimate, correct to the nearest whole number:

1. the number of animals infected after \(3\) days,
2. the number of days it will take for more than \(40\%\) of the animals to be infected.