Question

As baby boomers enter their golden years, the number of people afflicted with Alzheimer's disease is expected to rise dramatically. In a study published in the Journal of Neurology, the number of people with Alzheimer's disease in the United States age 65 years and over is projected to be

N(t) = 0.00525t² + 0.075t + 4.7 (0 ≤ t ≤ 4)

millon in decate t, where t = 0 corresponds to 2010.

(a) What is the projected number of people with Alzheimer's disease in the United States age 65 and over in 2020? (Round your answer to four decimal places.)
_________ million
(b) How fast is the number of people with Alzheimer's disease in the United States age 65 years and over projected to grow in 2020?
_________ million
(c) How fast is the rate of growth of people with Alzheimer's disease in the United States age 65 years and over projected to change in the period covered by the study?
_________ million per decade per decade.

Answer 1

Explanation:

Given that the number of people with Alzheimer's disease in the United States age 65 years and over is projected to be

`N(t) = 0.00525t^2 +0.075t+4.7,(0 ≤ t ≤ 4)`

where N is in millions where year 2010 corresponds to t=0

For 2020, 10 years lapsed hence t= 1

a)
`N(1) = 0.00525(1)^2 + 0.075(1) + 4.7\\=4.78025`

So 4.78025 million people

b) Growth = N(1)-n(0) =0.08025 million

c) N(4) = 5.084

Average rate of change = (5.084-4.7)/4 =0.096 million per decade