The number of Americans age 65 or older can be modeled asn(x)0.00082x3 0.059x2 0.183x + 34.42where output is measured in million people and x is the number of years since 2000, projections through 2050.t(a) What is the projected number of Americans 65 years of age and older in 2011? in 2040? (Round your answers to three decimal places.)million peoplemillion people20112040(b) What is the rate of change of the projected number in 2011? in 2040? (Round your answers to three decimal places.)million people per year2011million people per year2040(c) Calculate the percentage rate of change in the projected number in 2040. (Round your answer to two decimal places.)% per year

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Asked Oct 18, 2019
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The number of Americans age 65 or older can be modeled as
n(x)0.00082x3 0.059x2 0.183x + 34.42
where output is measured in million people and x is the number of years since 2000, projections through 2050.t
(a) What is the projected number of Americans 65 years of age and older in 2011? in 2040? (Round your answers to three decimal places.)
million people
million people
2011
2040
(b) What is the rate of change of the projected number in 2011? in 2040? (Round your answers to three decimal places.)
million people per year
2011
million people per year
2040
(c) Calculate the percentage rate of change in the projected number in 2040. (Round your answer to two decimal places.)
% per year
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The number of Americans age 65 or older can be modeled as n(x)0.00082x3 0.059x2 0.183x + 34.42 where output is measured in million people and x is the number of years since 2000, projections through 2050.t (a) What is the projected number of Americans 65 years of age and older in 2011? in 2040? (Round your answers to three decimal places.) million people million people 2011 2040 (b) What is the rate of change of the projected number in 2011? in 2040? (Round your answers to three decimal places.) million people per year 2011 million people per year 2040 (c) Calculate the percentage rate of change in the projected number in 2040. (Round your answer to two decimal places.) % per year

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Expert Answer

Step 1

Given,

The number of Americans aged 65 or above can be modelled as,
n(x)-0.00082x3 0.059x2 0.183x + 34.42
where x is the number of years since 2000.
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The number of Americans aged 65 or above can be modelled as, n(x)-0.00082x3 0.059x2 0.183x + 34.42 where x is the number of years since 2000.

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Step 2

(a)

(i) Number of people in 2011 is given by,
n(11)=0.00082 x 113 0.059 x 112 + 0.183 x 11 +34.42
= 42.481 million people
(ii) Number of people in 2040 is given by,
0.00082 x 403 0.059 x 4020.183 x 40 34.42
n(40)
83.660 millioп реople
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(i) Number of people in 2011 is given by, n(11)=0.00082 x 113 0.059 x 112 + 0.183 x 11 +34.42 = 42.481 million people (ii) Number of people in 2040 is given by, 0.00082 x 403 0.059 x 4020.183 x 40 34.42 n(40) 83.660 millioп реople

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Step 3

(b)

...
(i) Number of people in 2010 is given by,
n(10) 0.00082 x 103 0.059 x 102 0.183 x 10 +34.42
= 41.330 million people
Number of people in 2011 is given by,
п(11) 3 42.481 million people.
[calculaed in part (a)]
п(11) — п(10)
Rate of change of projected number in 2011 -
11 10
42.481 41.330
1
1.151 million people per year
=
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(i) Number of people in 2010 is given by, n(10) 0.00082 x 103 0.059 x 102 0.183 x 10 +34.42 = 41.330 million people Number of people in 2011 is given by, п(11) 3 42.481 million people. [calculaed in part (a)] п(11) — п(10) Rate of change of projected number in 2011 - 11 10 42.481 41.330 1 1.151 million people per year =

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Calculus

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