Question

The number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a relative rate of 12% per hour. Suppose that a sample culture has an initial population of 54 bacteria. Find the population predicted after three hours, according to the model.

Do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

The population predicted after three hours, according to the model, is approximately 70.7 bacteria.

Step-by-step explanation:

In exponential growth, the population increases at an accelerating rate. In this case, the number of bacteria is predicted to grow at a relative rate of 12% per hour. To find the population after three hours, we can use the formula:

P = P0(1 + r)t

Where P is the population after time t, P0 is the initial population, r is the relative growth rate, and t is the time in hours. Plugging in the given values, we have:

P = 54(1 + 0.12)3 ≈ 70.69

So, the population predicted after three hours is approximately 70.7 bacteria.