50=-0.26x^2-0.55x+91.81
We will use the Quadratic Formula to find the solutions.
2
&Quadratic equation: && ax^2+ bx+ c=0
&Solutions:&&x=- b±sqrt(b^2-4 a c)/2 aTo identify the coefficients, we need to rearrange our equation.
In this form we can identify the coefficients.
- 0.26x^2-55x+41.81= - 0.26x^2+( - 0.55)x+ 41.81
We see that a= - 0.26, b= - 0.55, and c= 41.81. Let's substitute these values into the Quadratic Formula.
Let's use a calculator to find approximate values of these solutions.
0.55+sqrt(43.7849)/-0.52&≈ -13.78
0.55-sqrt(43.7849)/-0.52&≈ 11.67
Since x represents the number of years after 2000, we need the positive solution.
The year in which the number of deaths caused by lung cancer is 50 per 100 000 corresponds to x=11.67.
c To find the year when the death rate is predicted to be 0, we solve a quadratic equation similar to the one we solved in Part B. This time we need to find the x that gives the prediction 0 instead of 50.
- 0.26x^2 - 0.55x+ 91.81=0
We see that a= - 0.26, b= - 0.55, and c= 91.81. Let's substitute these values into the Quadratic Formula.
Let's use a calculator to find approximate values of these solutions.
0.55+sqrt(95.7849)/-0.52&≈ -19.88
0.55-sqrt(95.7849)/-0.52&≈ 17.76
Since x represents the number of years after 2000, we need the positive solution.
The year in which the number of deaths caused by lung cancer is predicted to reduce to 0 corresponds to x=17.76.
2000+17.76=2017.76
According to the quadratic function, the death rate will be 0 in 2017.
This is not a reasonable prediction.
Even with a cure (which is currently not known), the success rate is unlikely to be 100 %.
