3 The number of members of a social networking site is modelled by \(m = 150 \mathrm { e } ^ { 2 t }\), where \(m\) is the number of members and \(t\) is time in weeks after the launch of the site.
- State what this model implies about the relationship between \(m\) and the rate of change of \(m\).
- What is the significance of the integer 150 in the model?
- Find the week in which the model predicts that the number of members first exceeds 60000 .
- The social networking site only expects to attract 60000 members.
Suggest how the model could be refined to take account of this.