- A new mobile phone is released for sale.
The total sales \(N\) of this phone, in thousands, is modelled by the equation
$$N = 125 - A \mathrm { e } ^ { - 0.109 t } \quad t \geqslant 0$$
where \(A\) is a constant and \(t\) is the time in months after the phone was released for sale.
Given that when \(t = 0 , N = 32\)
- state the value of \(A\).
Given that when \(t = T\) the total sales of the phone was 100000
- find, according to the model, the value of \(T\). Give your answer to 2 decimal places.
- Find, according to the model, the rate of increase in total sales when \(t = 7\), giving your answer to 3 significant figures.
(Solutions relying entirely on calculator technology are not acceptable.)
The total sales of the mobile phone is expected to reach 150000
Using this information, - give a reason why the given equation is not suitable for modelling the total sales of the phone.