7 It is claimed that the number of plants of a certain species in a particular locality is doubling every 9 years. The number of plants now is 42 . The number of plants is treated as a continuous variable and is denoted by \(N\). The number of years from now is denoted by \(t\).
- Two equivalent expressions giving \(N\) in terms of \(t\) are
$$N = A \times 2 ^ { k t } \quad \text { and } \quad N = A \mathrm { e } ^ { m t } .$$
Determine the value of each of the constants \(A , k\) and \(m\).
- Find the value of \(t\) for which \(N = 100\), giving your answer correct to 3 significant figures.
- Find the rate at which the number of plants will be increasing at a time 35 years from now.