A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 280.
(a) Find an expression for the number of bacteria after t hours.
(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest whole number.)
(c) Find the rate of growth after 2 hours. (Round your answer to the nearest whole number.)
(d) When will the population reach 10,000? (Round your answer to one decimal place.)