Suppose the population of a town is 17,400 and is growing 2% each year.
2 answers:
Answer:
Step-by-step explanation:
This is an exponential growth function of the form:
where a is the initial population and b is the growth rate. This could also be written as
which is a bit more accurate. We'll use that one. r is the percent growth: 2% for us.
Filling in the formula:
and then simplifying:
That's the model for this population. Filling in any number of years for x will give you the population y. Our time is 9 years:
Take care of the exponents first, giving us:
and then multiply to get
y = 20,794.6 or 20,794 people (since you can't have 6/10 of a person)
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Answer:
Step-by-step explanation:
A function satisfying the equation is said to be an even function. This denomination comes from the fact that the same relation is satisfied for functions of the form
with
even. Observe that if
is twice differentiable we can derivate using the chaing rule as follows:
implies
Applying the chain rule again we have:
implies
So we have that function is also an even function.
Answer:
a)
And we can find this probability using the complement rule:
b)
And we can find this probability uing the normal standard table:
c)
And we can find this probability with this difference:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the complement rule:
Part b
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability uing the normal standard table:
Part c
And we can find this probability with this difference:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.