Polynomial and rational functions can be used to model many phenomena in science, technology, and everyday life.
1. Give an example of a polynomial or rational function modeling a situation in that sector. [Hint: see the examples and exercises in the book.]
For example, the duration of efficacy of a vaccine against COVID-19 might be expressed by the function P(t)=5t/3t^2+3.
(t) months, and the ratio that can be expected to be effective one month after vaccination
P(t)=5t/3t^2+3
t=1
P(t)=5×(1)/3(1)^2+3
P(t)=5/3+3
P(t)=5/6
5/6 x 100 = 83.3333333
Therefore, the vaccine is up to 83.3% effective in the first month.
(t) months, and the ratio that can be expected to be effective 2 months after vaccination
P(t)=4t/3t^2+3
t=2
P(t)=5×(2)/3(2)^2+3
P(t)=10/12+3
P(t)=10/15=2/3
2/3 x 100 = 66.6666667
Therefore, the vaccine was 66.7% effective 2 months after vaccination, about 17% less effective than at 1 month.
(t) months, and the ratio that can be expected to be effective 10 months after vaccination
P(t)=5t/3t^2+3
t=10
P(t)=5×(10)/3(10)^2+3
P(t)=50/300+3
P(t)=50/303
50/303 x 100 = 16.5016502
Therefore, the vaccine was 16.5% effective 10 months after vaccination, about 67% less effective than at 1 month.
2. Go to www.desmos.com/calculator, write your equation, or function, and develop your explanation using the properties of graphs.
Here is the graph I created using www.desmos.com/calculator:
In the medical industry, the effects of drugs and vaccines are verified and evaluated through these methods. The results obtained in this way help determine the duration of efficacy of the vaccine, the number of doses, and the frequency of vaccination. (253 words)
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