Predicting growth from an exponential model

A culture contains \(N=Ab^t\) cells after \(t\) hours, where \(A>0\) and \(b>1\). There are 90 cells after 1 hour and 250 cells after 3 hours.

1. Use a straight-line form to find \(A\) and \(b\).[4]
2. Estimate the number of cells after 4 hours, to the nearest whole number.[2]
3. Find when the model predicts 500 cells, correct to 3 significant figures.[2]