6.21 The population of Americans age 55 and older as a percentage of the total p

Question

6.21

The population of Americans age 55 and older as a percentage of the total population is approximated by the function f(t) 10.72 (0.9t 10) 0.3 (0 sts 20) where t is measured in years, with 0 corresponding to the year 2000.t (Round your answers to one decimal place At what rate was the percentage of Americans age 55 and older changing at the beginning of 2003? X per year At what rate will the percentage of Americans age 55 and older be changing in 2018? per year What will be the percentage of the population of Americans age 55 and older in 2018? 28.6

Explanation / Answer

f(t) = 10.72*(0.9*t+10)^0.3

rate of change = f'(t)
f'(t) = 10.72*0.3*(0.9*t+10)^(0.3-1)
      = 3.216*(0.9*t+10)^(-0.7)
  
a)
at the begining of 2003 means t=2
f'(2) = 3.216*(0.9*2+10)^(-0.7)
      = 0.571
Answer: 0.571 0r 57.1 %

b)
hete t=18

f'(2) = 3.216*(0.9*18+10)^(-0.7)
      = 0.327
Answer: 0.327 0r 32.7 %

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