The number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a relative rate of 15% per hour. Suppose that a sample culture has an initial population of 22 bacteria. Find the predicted population after six hours.
amount = 22 e^(6(.15))
= 22(2.4596..) = appr 54 of them
To find the predicted population after six hours using the continuous exponential growth model, we can use the formula:
P(t) = P₀ * e^(rt)
Where:
P(t) = predicted population at time t
P₀ = initial population
e = Euler's number (approximately 2.71828)
r = relative growth rate (expressed as a decimal)
t = time elapsed
In this case, the initial population (P₀) is 22 bacteria, and the relative growth rate (r) is 15% per hour. However, we need to convert the relative growth rate to a decimal, so r = 15% = 0.15.
Now, we can substitute the values into the formula and solve for P(6):
P(6) = 22 * e^(0.15 * 6)
To calculate the predicted population after six hours, follow these steps:
Step 1: Raise Euler's number (e) to the power of (0.15 * 6):
e^(0.15 * 6) ≈ 2.598
Step 2: Multiply the result from step 1 by the initial population (22):
2.598 * 22 ≈ 57.15
Therefore, the predicted population after six hours is approximately 57 bacteria.
To find the predicted population after six hours using a continuous exponential growth model with a relative growth rate of 15% per hour, we can use the following formula:
P(t) = P(0) * e^(rt)
Where:
P(t) = predicted population after time t
P(0) = initial population
e = Euler's number (approximately 2.71828)
r = relative growth rate per unit of time
t = time
In this case, the initial population (P(0)) is given as 22 bacteria, the relative growth rate (r) is 15% per hour, and the time (t) is six hours.
Plugging the values into the formula, we get:
P(6) = 22 * e^(0.15 * 6)
Now we can calculate the predicted population after six hours.