THIS IS REALLY EASY I JUST NEED HELP
1 answer:
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Answer:
Step-by-step explanation:
We are given that there is an exponential decay.
Also, the decrease is of constant rate 7.9% i.e. 0.079 each year.
Since, the initial amount of the species is atleast 26 million.
Thus, the inequality for the corresponding model will be, ,
where t is the time period for the decay and P is the population.
Moreover, is is given that the population cannot be less than 2 million.
So, we get, .
Hence, the inequalities to determine the possible number of insects over time are given by,
.
This is a permutation question because we care about the order.
We can demonstrate this by letting each person be a person in the pie eating contest.
A B C D E F G H I J K
_ _ _
Now, there are 11 ways for the first prize to be won, since there are no restrictions upheld. Let's say A wins the first prize.
B C D E F G H I J K
A _ _
Now, assuming prizes aren't shared, there are only ten people left to win the second prize.
Using this logic, then we can say that nine can win the third prize.
Thus, our answer is 11 · 10 · 9 = 990 ways.
However, this method works for this question.
What happens when the number of places we want gets significantly larger?
That's when we introduce the permutation formula.
We know that 11·10·9·8·7·6·5·4·3·2·1 = 11!, but we don't want 8! of them.
This is the formula for permutation.
We can demonstrate this by letting each person be a person in the pie eating contest.
A B C D E F G H I J K
_ _ _
Now, there are 11 ways for the first prize to be won, since there are no restrictions upheld. Let's say A wins the first prize.
B C D E F G H I J K
A _ _
Now, assuming prizes aren't shared, there are only ten people left to win the second prize.
Using this logic, then we can say that nine can win the third prize.
Thus, our answer is 11 · 10 · 9 = 990 ways.
However, this method works for this question.
What happens when the number of places we want gets significantly larger?
That's when we introduce the permutation formula.
We know that 11·10·9·8·7·6·5·4·3·2·1 = 11!, but we don't want 8! of them.
This is the formula for permutation.