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

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joaobezerra joaobezerra · Answer 1 · 2022-01-26T11:05:46+01:00

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

[tex]a(n) = -5.6n + 16.7[/tex]

A linear function is modeled by:

[tex]y = mx + b[/tex]

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 [tex]b = 16.7[/tex]

The percentage is decreasing by 5.6% each year, hence the slope is [tex]m = -5.6[/tex].

Then, the equation is:

[tex]y = mx + b[/tex]

[tex]a(n) = -5.6n + 16.7[/tex]

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