quadrane Atmospheric CO2 The llic 316.8 62. Concentration of 0.90 10x in per mil
ID: 3408824 • Letter: Q
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quadrane Atmospheric CO2 The llic 316.8 62. Concentration of 0.90 10x in per mil- f(r) 0098 2 dioxide parts models the worldwide atmospheric concentration of carbon the year If this lion Oppm) period 2009, where r concentration in 2020 model continues to hold, what will be the atmospheric Co2 (Source: of Energy.) Americans on shoe Spending on shoes and Clothing The total amount spent by 63. and clothing from 2000 to 2009 can be modeled by f(r) 4.979x 71.73 x 97.29, where x o represents 2000 and f(x) is in billions of dollars. Based on this model, in what year did spending on shoes and clothing reach a maximum? (Source: Bureau of Economic Analysis.) Accident Rate According to data from the National Highway Traffic Safety Ad- 64. ministration, the accident rate as a function of the age of the driver in years x can be approximated by the function f(x) 0.0232x2 2.28 x 60.0, for 16 s x s 85. Find both the age at which the accident rate is a minimum and the minimum rate. AIDS Cases in the United States Year AIDS Cases Year AIDS Cases The table* lists the total (cumula- tive) number of AIDS cases diao. 1990 193Explanation / Answer
64. accident rate as function of age f(x) = 0.0232x^2 - 2.28 x + 60.0
for 16< = x <= 85
Minimum of accident rate: For a quadratic equation y = ax^2 +bx +c minimum occurs at
x= -b/2a .compare with :standard equation with f(x) = 0.0232x^2 - 2.28 x + 60.0
x= -( -2.28)/(2*0.0232) = 49.13 years
Minimum rate of accident occurs at x = 49.13 years
Minimum accident rate ( plug x= 49.13 years) = 0.0232(49.13)62 -2.28( 49.13) +60
= 3.982
x =
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