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?
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.