Question

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 2.8%

per hour. How many hours does it take for the size of the sample to double?
Note: This is a continuous exponential growth model.
Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answer 1

It takes approximately 24.73 hours for the population to double.

Step-by-step explanation:

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 2.8% per hour.

To determine how many hours it would take for the population to double in size, we can use the formula derived from the continuous exponential growth model: N(t) = N₀e^(rt), where N(t) is the future number of bacteria, N₀ is the initial number of bacteria, r is the growth rate, and t is the time in hours.

We can assume N₀ to be 1 for simplification since we are interested in the doubling time (when the population becomes 2N₀), and the equation simplifies to 2 = e^(0.028t).

Taking the natural logarithm of both sides gives us ln(2) = 0.028t.

Solving for t, we get t = ln(2)/0.028.

Therefore, it takes approximately 24.73 hours for the population to double.