In 1966, the U.S. Surgeon General's health warnings began appearing on cigarette packages. Data gathered after 1965 indicate that public awareness of the health hazards of smoking has had some effect on consumption of cigaretts.
The percentage, p, of the total population (18 and older) who smoked t years after 1965 can be approximated by the model p=0.55t + 41.67, where t is the number of years after 1965.
Note that t=0 corresponds to the year 1965, t=9 corresponds to 1974, etc.
a. Determine the percentage of the population who smoked in 1991 (t=16)
b. Use the formula to determine the year when the percentage of smokers will be 15% (p=15)?
I think you have an error. Your percentage of smokers INCREASES with time.
To determine the percentage of the population who smoked in 1991 (t=16), we can use the given formula p = 0.55t + 41.67. We substitute t with 16 and solve for p.
a. Substitute t = 16 into the formula: p = 0.55(16) + 41.67
p = 8.8 + 41.67
p ≈ 50.47
Therefore, the percentage of the population who smoked in 1991 (t=16) is approximately 50.47%.
b. To determine the year when the percentage of smokers will be 15% (p=15), we can use the same formula and solve for t.
15 = 0.55t + 41.67
First, let's subtract 41.67 from both sides:
15 - 41.67 = 0.55t
-26.67 = 0.55t
To isolate t, divide both sides by 0.55:
-26.67 / 0.55 = t
t ≈ -48.49
Since the value of t represents the number of years after 1965, a negative value doesn't make sense in this context. Therefore, it's not possible to determine a year when the percentage of smokers will be exactly 15% using this formula.
However, if you assume the model continues to be accurate beyond the provided data range (i.e., beyond 1991), you could consider rounding t to the nearest whole number to estimate the year when the percentage of smokers reaches or approaches 15%. For example, if t is rounded to 49, it would correspond to the year 1991 + 49 = 2040. But please note that this estimation is not necessarily accurate and should be treated as an approximation.