A 10 year research program is being carried out on two penguin rookery populations in Tasmania. Rookery A had 2000 penguins at the start of the study and the population has been decreasing by 5% per year. Rookery B had 3000 penguins initially and this population has been decreasing by 10% per year.

a) Calculate how long it will take for the two populations to be the same.

b) Find this actual figure.

State any assumptions and use algebra, logarithms and other mathematics means (not a graphics calculator) to assist in your solution.