- The prices of two precious metals are being monitored.
The price per gram of metal \(A , \pounds V _ { A }\), is modelled by the equation
$$V _ { A } = 100 + 20 \mathrm { e } ^ { 0.04 t }$$
where \(t\) is the number of months after monitoring began.
The price per gram of metal \(B , \pounds V _ { B }\), is modelled by the equation
$$V _ { B } = p \mathrm { e } ^ { - 0.02 t }$$
where \(p\) is a positive constant and \(t\) is the number of months after monitoring began.
Given that \(V _ { B } = 2 V _ { A }\) when \(t = 0\)
- find the value of \(p\)
When \(t = T\), the rate of increase in the price per gram of metal \(A\) was equal to the rate of decrease in the price per gram of metal \(B\)
- Find the value of \(T\), giving your answer to one decimal place.
(Solutions based entirely on calculator technology are not acceptable.)