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Answer:
The population size after eight days is about 265
Step-by-step explanation:
This is an example of an exponential growth model. A quantity <em>y</em> that grows or decays at a rate proportional to its size fits in an equation of the form
where k is a positive constant. Its solutions have the form
,
where is the initial value of y.
The population size can be calculated by using the below formula:
where
is the population on day zero.
Let t be the time in days,
We know from the information given that:
- k = 0.4964 per member per day and
- The day zero (t = 0) the population size is 5 (P(0) = 5)
To find the population size after eight days
Substitute P(0) = 5, k=0.4964 in
Then
Now we calculate P(t) when t = 8 days
Therefore the population size after eight days is about 265