Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of
11%
per hour. Suppose also that a sample culture of
1000
bacteria is obtained from this population. Find the size of the sample after two hours. Round your answer to the nearest integer.
n = 1000 * e^(.11 * 2)
To find the size of the sample after two hours using the continuous exponential growth model, we can use the following formula:
N(t) = N0 * e^(rt),
where N(t) represents the size of the sample at time t, N0 is the initial size of the sample, e is the mathematical constant approximately equal to 2.71828, r is the growth rate parameter, and t is the time in hours.
In this case, we know that the initial size of the sample is 1000 bacteria, the growth rate parameter is 11% per hour (which can be expressed as 0.11), and we want to find the size of the sample after two hours.
Substituting the given values into the formula, we have:
N(2) = 1000 * e^(0.11 * 2).
Calculating this expression, we get:
N(2) ≈ 1000 * e^(0.22).
Using a calculator, we find that e^(0.22) is approximately 1.2466.
Therefore, the size of the sample after two hours is approximately:
N(2) = 1000 * 1.2466 ≈ 1246.6
Rounding this to the nearest integer, the size of the sample after two hours is approximately 1247 bacteria.