- A population of a rare species of toad is being studied.
The number of toads, \(N\), in the population, \(t\) years after the start of the study, is modelled by the equation
$$N = \frac { 900 \mathrm { e } ^ { 0.12 t } } { 2 \mathrm { e } ^ { 0.12 t } + 1 } \quad t \geqslant 0 , t \in \mathbb { R }$$
According to this model,
- calculate the number of toads in the population at the start of the study,
- find the value of \(t\) when there are 420 toads in the population, giving your answer to 2 decimal places.
- Explain why, according to this model, the number of toads in the population can never reach 500