5. The number of bacteria on a surface is being monitored.
The number of bacteria, \(N\), on the surface, \(t\) hours after monitoring began is modelled by the equation
$$\log _ { 10 } N = 0.35 t + 2$$
Use the equation of the model to answer parts (a) to (c).
- Find the initial number of bacteria on the surface.
- Show that the equation of the model can be written in the form
$$N = a b ^ { t }$$
where \(a\) and \(b\) are constants to be found. Give the value of \(b\) to 2 decimal places.
- Hence find the rate of growth of bacteria on the surface exactly 5 hours after monitoring began.