The population of a city is observed as growing exponentially according to the function P(t) = P0_{e}^{kt}, where the population doubled in the first 50 years.
(a) Find k to three decimal places.
(b) By what factor (to two decimal places) will the original population have grown in the first 125 years?
(c) When will the original size of the population have grown by a factor of ten?