Answer:(a) N ≈ 3,900
(b) N ≈ 38,120
Step-by-step explanation:
To calculate the number of bacteria in the colony at a given time using the exponential growth formula N = Noe^(kt), where N represents the number of bacteria, No is the initial number of bacteria, e is the base of the natural logarithm, k is the growth rate, and t is the time in hours.
Given:
No = 400 (initial number of bacteria)
k = 19% = 0.19 (growth rate per hour)
a.) How many bacteria should be in the colony in 12 hours?
N = Noe^(kt)
Substituting the given values into the formula:
N = 400 * e^(0.19 * 12)
Calculating the value:
N ≈ 400 * e^(2.28)
N ≈ 400 * 9.7492
N ≈ 3,899.68
Rounding to the nearest integer:
N ≈ 3,900
Therefore, there should be approximately 3,900 bacteria in the colony after 12 hours.
b.) How many bacteria in one day?
To calculate the number of bacteria in one day (24 hours), we'll use the same formula.
N = Noe^(kt)
Substituting the values:
N = 400 * e^(0.19 * 24)
Calculating the value:
N ≈ 400 * e^(4.56)
N ≈ 400 * 95.299
Rounding to the nearest integer:
N ≈ 38,120
Therefore, there should be approximately 38,120 bacteria in the colony after one day.