Final answer:
The exercise requires using the population growth model to calculate the time needed for a culture of bacteria to double using the exponential growth formula. By finding the growth rate first, we can then estimate the doubling time.
Step-by-step explanation:
The question involves a population growth model used to calculate the time required for a bacterial culture to double in size. We know that the initial population is 8600 bacteria and after 1 hour, the population grows to 10,000 bacteria. To determine after how many hours the number of bacteria will double, we can use the concept of exponential growth and the data provided to find the growth rate.
Firstly, we calculate the growth rate (r) using the formula:
N(t) = N0ert
Where N(t) is the population at time t, N0 is the initial population, e is the base of the natural logarithm, and r is the growth rate. Using the data 10,000 = 8600er, we can find r. After finding r, we can then use the same formula to solve for t when the population N(t) is double the initial population (2 * 8600).
Through this calculation, we can answer the question and provide the time in hours, rounded to one decimal place.