Imagine a pond. In it sits one lilypad, which reproduces once a day. Each of its offspring also reproduces once a day, doubling
1 answer:
Answer: On the 29th day
Step-by-step explanation:
According to this problem, no lilypad dies and the lilypads always reproduce, so we can apply the following reasoning.
On the first day there is only 1 lilypad in the pond. On the second day, the lilypad from the first reproduces, so there are 2 lilypads. On day 3, the 2 lilypads from the second day reproduce, so there are 2×2=4 lilypads. Similarly, on day 4 there are 8 lilypads. Following this pattern, on day 30 there are 2×N lilypads, where N is the number of lilypads on day 29.
The pond is full on the 30th day, when there are 2×N lilypads, so it is half-full when it has N lilypads, that is, on the 29th day. Actually, there are lilypads on the 30th, and
lilypads on the 29th. This can be deduced multiplying succesively by 2.
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Domain = {-3, 2}
Range = All real numbers
We can represent the range in interval notation as which is basically saying
. The range is all real numbers due to the arrows meaning the graph extends up and down forever. So any y value is possible.
Notice with the domain we only have 2 valid x values -3 and 2. No other x values are allowed. Normally we use an interval of some kind to set up the domain, but we only have a set of values instead. The curly braces indicate "set".
Answer:
0.1606 = 16.06% probability that the number of births in any given minute is exactly five.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
In this question:
We only have the mean during an interval, and this is why we use the Poisson distribution.
The mean number of births per minute in a given country in a recent year was about 6.
This means that
Find the probability that the number of births in any given minute is exactly five.
This is P(X = 5). So
0.1606 = 16.06% probability that the number of births in any given minute is exactly five.