Question

The prevalence of cigarette smoking in the united states is in decline if the percentage of smokers in 2014 was 16.7% and the percentage is decreasing by 5.6% each year, write the explicit formula for the sequence whose terms represent the percentage of americans who smoke n years after 2014.
1. an=-16.7n-5.6
2 an=16.7n-5.6
3. an=-5.6n+16.7
4 an=5.6n+16.7

Answer 1

The linear formula for the sequence whose terms represent the percentage of americans who smoke n years after 2014 is:

$a(n) = -5.6n + 16.7$

What is a linear function?

A linear function is modeled by:

$y = mx + b$

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0, and for a time-dependent function, can also be interpreted as the initial value.

In this problem:

• The percentage of smokers in 2014 was 16.7%, hence the initial value is $b = 16.7$

• The percentage is decreasing by 5.6% each year, hence the slope is $m = -5.6$.

Then, the equation is:

$y = mx + b$

$a(n) = -5.6n + 16.7$

You can learn more about linear functions at brainly.com/question/24808124