In januaray 1994 the number of smokers in benton county was 4000 people.

Question

since this time the number of people that smoke cigarettes in this county have been decreasing. The relationshio between Y , the number of smokers and N , The number of years since 1994 can be modeled with either a linear model or an exponential model. The linear model has a constant decrease of 150 smokers per year. The exponential has a decrease of 5% of the smokers per year. For each model , determine an equation that expresses Y in term of N. which model indicates a higher number of smokers in benton county in 2010?

Answer 1

Hi Jake,

 

For the linear model, we start with 4000 smokers, and after 1 year have 150 less, after 2 years have 2*150 less, 3 years have 3*150 less, ... Thus the equation for the number of people still smoking is

 

   Y = 4000 - 150 * N

 

For the exponential model, we again start with 4000 smokers, and after 1 year have 5% less, so 95% (0.95) are still smoking; after 2 years 95% of (95 % of 4000) are smoking; after 3 years, 95% of 95% of 95% ... Thus the exponential equation is

 

   N = 4000 * (0.95 ^ N)

 

where "^" is the exponentiation operator.

 

By the year of 2010 (let's use the end of the year), that would be 16 years from 1994. So N=16. If we evaluate the linear equation we have

 

   N = 4000 - 150 * 16 = 4000 - 2400 = 1600 still smoking

 

and for the exponential equation

 

   N = 4000 * (0.95 ^ 16) = 4000 * 0.440127 = 1760.5 still smoking

 

I don't think "half a person" can be smoking, so we'll say 1760 still smoking with the exponential model.

 

Hope this helps you.