Final answer:
The initial size of the bacteria culture was 500 bacteria. The doubling period is 15 minutes. The population after 85 minutes is approximately 5632 bacteria. The population will reach 14000 bacteria after approximately 60 minutes.
Step-by-step explanation:
To find the initial size of the bacteria culture, we can use the formula for exponential growth: N = N0 * 2^(t/d), where N is the final count, N0 is the initial count, t is the time, and d is the doubling period. Plugging in the given values, we have 1000 = N0 * 2^(30/15). Solving for N0, we find that the initial size of the culture was 500 bacteria.
The doubling period can be found by dividing the time it takes for the count to increase by a factor of 2. In this case, it is 30 - 15 = 15 minutes.
To find the population after 85 minutes, we can use the formula N = N0 * 2^(t/d), where N is the final count, N0 is the initial count, t is the time, and d is the doubling period. Plugging in the values, we have N = 500 * 2^(85/15). Solving for N, we find that the population after 85 minutes is approximately 5632 bacteria.
To find when the population will reach 14000 bacteria, we can use the formula N = N0 * 2^(t/d). Plugging in the values, we have 14000 = 500 * 2^(t/15). Solving for t, we find that the population will reach 14000 bacteria after approximately 60 minutes.