Question

10 interpreting function notation let h(x) be the percent of u.s. households with internet use x years after 1980. explain the meaning of each statement. a. h(27)=61.7 b. h(4)=k c. h(37)>h(30) d. h(17)+h(21)=h(29)

Explanation:

• a. $H(27) = 61.7$ means that 27 years after 1980 (i.e., in the year 2007), 61.7% of U.S. households had Internet use.
• b. $H(4)=k$ means that 4 years after 1980 (i.e., in 1984), $k$ percent of U.S. households had Internet use.
• c. $H(37)>H(30)$ means that the percentage of U.S. households with Internet use 37 years after 1980 (i.e., in 2017) is greater than the percentage 30 years after 1980 (i.e., in 2010).
• d. $H(17)+H(21)=H(29)$ would imply that the sum of the percentage of U.S. households with Internet use 17 years after 1980 (i.e., in 1997) and 21 years after 1980 (i.e., in 2001) is equal to the percentage of U.S. households with Internet use 29 years after 1980 (i.e., in 2009). However, in reality, this may or may not be true depending on the actual function $H(x)$.

Answer:

• a. In 2007, 61.7% of U.S. households had Internet use.
• b. In 1984, $k$ percent of U.S. households had Internet use.
• c. The percentage of U.S. households with Internet use in 2017 is greater than that in 2010.
• d. The sum of the percentage of U.S. households with Internet use in 1997 and 2001 may or may not be equal to the percentage in 2009.