A population, \(P\) million, is modelled by

\(P=Ab^t,\)

where \(t\) is the number of years after 1 January 2000. The population was \(40\) million on 1 January 2010 and \(45\) million on 1 January 2013.

(a) Find \(b\), correct to 2 decimal places, and find \(A\), correct to the nearest integer.

(b) Use your values of \(A\) and \(b\) to estimate the population on 1 January 2020.

(c) Use your values of \(A\) and \(b\) to find the first year in which the population is predicted to exceed \(100\) million.