Question

The number of people aged 18 to 24 years old who smoked decreased according to the CDC. In 2005, 24.7% of the age group smoked, and that number declined to 19.3% in 2010.Assume the rate of change is linear keep a running difference and round each smoker to the nearest tenth

Answer 1

Finding percentages

If each year the percentage changes the same amount and we have six years from 2005 to 2010:

1. 2005

2. 2006

3. 2007

4. 2008

5. 2009

6. 2010

If we want to know that difference between years, then we have to divide the total change in five parts:

`\begin{gathered} 24.7-19.3=5.4 \\ (5.4)/(5)=1.08 \end{gathered}`

Then it changes 1.08% each year. So if we substract that quantity each year from 2005, at 2010we should have 19.3%:

1. 2005: 24.7%

2. 2006: 24.70% - 1.08% = 23.62%

3. 2007: 23.62% - 1.08% = 22.54%

4. 2008: 22.54% - 1.08% = 21.46%

5. 2009: 21.46% - 1.08%= 20.38%

6. 2010: 20.38% - 1.08% = 19.3%

Now we round each to the nearest tenth:

1. 2005: 24.7%

2. 2006: 23.62% ≅ 23.6%

3. 2007: 22.54% ≅ 22.5%

4. 2008: 21.46% ≅ 21.5%

5. 2009: 20.38% ≅ 20.4%

6. 2010: 19.3%