Question

At the beginning of a study, a certain culture of bacteria has a population of 460. The population grows according to a continuous exponential growth model. After 15 days, there are 506 bacteria. What is the growth rate of the bacteria population?

1) 0.05
2) 0.1
3) 0.15
4) 0.2

Answer 1

To find the growth rate of the bacteria population, we can use the continuous exponential growth formula. Plugging in the given values, we can solve for the growth rate. The growth rate of the bacteria population is approximately 0.036.

Step-by-step explanation:

To find the growth rate of the bacteria population, we can use the continuous exponential growth formula:

N = N0 * e^(rt)

Where N is the final population, N0 is the initial population, e is the base of the natural logarithm (approximately 2.718), r is the growth rate, and t is the time period in days.

From the given information, we know that the initial population (N0) is 460 and the final population (N) after 15 days is 506. Plugging these values into the formula, we get:

506 = 460 * e^(15r)

Dividing both sides by 460, we get:

e^(15r) = 506/460

Taking the natural logarithm of both sides, we get:

15r = ln(506/460)

Finally, dividing both sides by 15, we find:

r = ln(506/460)/15 ≈ 0.036

Therefore, the growth rate of the bacteria population is approximately 0.036.