Final answer:
The population model for bacteria after time t is P = 15000 x (2^(t/1.5)), where t is the number of hours after 3 pm and the doubling time is 1 1/2 hours.
Step-by-step explanation:
To model the population of bacteria at time t hours after 3 pm with a starting population of 15,000 and a doubling time of 1 1/2 hours, you can use the formula P = 15000 × (2^(t/1.5)).
The exponent t/1.5 represents the number of doubling periods that have passed since 3 pm, as each period is 1 1/2 hours long. For example, after 3 hours, which is 2 periods, the population will have doubled twice, leading to P = 15000 × (2^2) = 15000 × 4 = 60000 bacteria.