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GreenHerbz206
16.10.2020 •
Mathematics
Which expressions are equivalent to the given expression?
√252
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Ответ:
Ответ:
Part A)
About 0.51% per year.
Part B)
About 0.30% per year.
Part C)
About 28.26%.
Step-by-step explanation:
We are given that the population of Americans age 55 and older as a percentange of the total population is approximated by the function:
Where t is measured in years with t = 0 being the year 2000.
Part A)
Recall that the rate of change of a function at a point is given by its derivative. Thus, find the derivative of our function:
Rewrite:
We can use the chain rule. Recall that:
Let:
Then from the Power Rule:
Thus:
Substitute:
And simplify:
For 2002, t = 2. Then the rate at which the percentage is changing will be:
Contextually, this means the percentage is increasing by about 0.51% per year.
Part B)
Evaluate f'(t) when t = 17. This yields:
Contextually, this means the percetange is increasing by about 0.30% per year.
Part C)
For this question, we will simply use the original function since it outputs the percentage of the American population 55 and older. Thus, evaluate f(t) when t = 17:
So, about 28.26% of the American population in 2017 are age 55 and older.