Question

in 2005 the percentage of female adults who smoked in the us was 20.9%. in 2013 the percentage was 17.8%, assuming tend was linear, when will the percentage hit 12%

Answer 1

The percentage is expected to hit 12% around the year 2030.

Step-by-step explanation:

To determine when the percentage of female adults who smoke in the US will hit 12%, we can assume a linear trend between 2005 and 2013.

First, we need to find the rate of decrease in the percentage:

Rate of decrease = (17.8% - 20.9%) / (2013 - 2005) = -0.31% per year

Next, we can use this rate to determine the number of years it takes for the percentage to reach 12%:

(12% - 17.8%) / -0.31% = 17.42 years

Therefore, the percentage is expected to hit 12% approximately 17.42 years after 2013, which would be around the year 2030.

Answer 2

2028

Step-by-step explanation:

Given:

U₂₀₀₅ = 20.9%

U₂₀₁₃ = 17.8%

Uₙ = 12%

U₂₀₁₃ - U₂₀₀₅ = [U₁ + (2013 - 1)d] - [U₁ + (2005 - 1)d]

17.8% - 20.9% = U₁ + 2012d - U₁ - 2004d

8d = -3.1%

d = -0.3875%

Uₙ - U₂₀₁₃ = [U₁ + (n - 1)d] - [U₁ + (2013 - 1)d]

12% - 17.8% = U₁ + (n - 1)d - U₁ - 2012d

-5.8% = (n - 1 - 2012)d

n - 2013 = -5.8% ÷ (-0.3875%)

n = 15 + 2013

n = 2028