(d) Graph the population function and estimate the time for the population to reach 50,000. 30. A bacterial culture starts with 500 bacteria and doubles in size every half hour. (a) How many bacteria are there after 3 hours? (b) How many bacteria are there after t hours? (c) How many bacteria are there after 40 minutes? (d) Graph the population function and estimate the time for the population to reach 100,000. 31. The half-life of bismuth-210, 20 Bi, is 5 days. (a) If a sample has a mass of 200 mg, find the amount remaining after 15 days. (b) Find the amount remaining after t days. (c) Estimate the amount remaining after 3 weeks. (d) Use a graph to estimate the time required for the mass to be reduced to 1 mg. 32. An isotope of sodium, 2Na, has a half-life of 15 hours.

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