- A scientist is studying the number of bees and the number of wasps on an island.
The number of bees, measured in thousands, \(N _ { b }\), is modelled by the equation
$$N _ { b } = 45 + 220 \mathrm { e } ^ { 0.05 t }$$
where \(t\) is the number of years from the start of the study.
According to the model,
- find the number of bees at the start of the study,
- show that, exactly 10 years after the start of the study, the number of bees was increasing at a rate of approximately 18 thousand per year.
The number of wasps, measured in thousands, \(N _ { w }\), is modelled by the equation
$$N _ { w } = 10 + 800 \mathrm { e } ^ { - 0.05 t }$$
where \(t\) is the number of years from the start of the study.
When \(t = T\), according to the models, there are an equal number of bees and wasps. - Find the value of \(T\) to 2 decimal places.