Final answer:
To determine the remaining bacteria after 22 hours, the decay constant must be calculated using the exponential decay formula and then applied to find the population size after 22 hours using the same formula.
Step-by-step explanation:
You've asked how many bacteria will remain after 22 hours if a bacteria population declined from 440,000 to 900 in 48 hours. To solve this, we can use the formula for exponential decay, which is N = N0 * e^(-kt), where:
- N is the remaining amount after time t,
- N0 is the initial quantity,
- e is the base of the natural logarithms (approx. 2.71828),
- k is the decay constant,
- t is the time period.
First, we need to determine the decay constant k using the given initial amount and the remaining amount after 48 hours:
N0 = 440,000
N = 900
t = 48 hours
We can rewrite the decay formula to solve for k:
k = -ln(N/N0)/t
Inserting the given values:
k = -ln(900/440,000)/48
Once we determine k, we can then calculate the number of bacteria after 22 hours using the decay formula again:
N = 440,000 * e^(-k * 22)
It's important to have a scientific calculator or software to accurately compute the values of e raised to the power of the negative product of k and t.