On her way home from the laboratory, Duru realized that she left a test tube containing 50,000 bacteria in the lab. Each minute that passes 1/3 the total number of bacteria duplicate. If the number of bacteria reaches 100,000 the test tube will explode! Naturally, she turned around and rushed back to the lab. It took Duru t minutes to return to the lab, and she found the test tube intact.
Write an inequality in terms of t that models the situation.