6. The graph below shows the projected number of people aged 65 and over in the
ID: 2890945 • Letter: 6
Question
6. The graph below shows the projected number of people aged 65 and over in the United States with Alzheimer's disease. (5 points each) a) Find and interpret the average rate of change between 2005 and 2015 in the number of people aged 65 and over in the United States with Alzheimer's disease.(SHOW WORK for full credit). HINT: Pay attention to how the graph is scaled and labeled The average rate of change is 0.1 so the number of people aged 65 and over in the US with Alzheimer's disease increased by about 0.2 million per year between 2005 and 2015. b) Estimate and interpret the derivative in 2015. (SHOW WORK for full credit). In 2015 the the number of people aged 65 and over in the US with Alzheimer's disease was increasing by about 0.1 million 14 12 2010 2020 2030 2040 205 earExplanation / Answer
6)
a)
from the graph
in year 2005 number of people over age 65 with alzheimer's diseease are 4.4 million
in year 2015 number of people over age 65 with alzheimer's diseease are 5.4 million
average rate of change =[5.4-4.4]/(2015-2005)
average rate of change =1/10
average rate of change =0.1
so the number of people in us aged over 65 with alzheimer's disease are increased by about 0.1 million per year between 2005 and 2015
(b)
in year 2010 number of people over age 65 with alzheimer's diseease are 5 million
in year 2015 number of people over age 65 with alzheimer's diseease are 5.4 million
in year 2020 number of people over age 65 with alzheimer's diseease are 6 million
between 2010,2015, average rate of change =[5.4-5]/(2015-2010) =0.08
between 2015,2020, average rate of change =[6-5.4]/(2020-2015) =0.12
derivative in 2015 =[0.08+0.12]/2
derivative in 2015 =0.1
in the year 2015 number of people in us aged over 65 with alzheimer's disease are increasing by about 0.1 million per year
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