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Question 1195418: Year-Percent of US households with TV
1951-23.5
1958-83.2
1978-98.0
The table shows the percent of US households with TV for three different years. From 1951 to 1958, the percent of US households with TV increased linearly over time and can be modeled by a linear function P. From 1958 to
1978, the percent of US households with TV also increased linearly, but at a different rate. Based on the information given, which of the
following is closest to the percent of US households with TV in 1962?
A) 91.3%
B) 90.6%
C) 87.4%
D) 86.2%
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
From 1958 to 1978, a span of 20 years, the percentage increased by 14.8%, from 83.2% to 98.0%.
From 1958 to 1962 is a span of 4 years, so 1962 was 4/20 = 1/5 of the way from 1958 to 1978. Since the rate of increase was constant, the increase in percentage from 1958 to 1962 was 1/5 of 14.8%, or about 3%. So
ANSWER: The percentage in 1962 was about 83.2% + 3.0% = 86.2%. Answer D
More formally....
Slope (i.e., rate of change) from 1958 to 1978 = (change in %) divided by (change in years) = (98.0-83.2)/(1978-1958) = 14.8/20 or about 15/20 = 3/4. So the percentage increased by about 3% every 4 years.
1962 was 4 years after 1958, so the percentage in 1962 was about 3% greater than in 1958: 83.2% + 3% = 86.2%.
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