On solving the inequality, 9 weeks of exercise are necessary to lower the individual’s resting heart rate below 70 beats per minute.
An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
[tex]-0.1x^{3} + 0.6x^{2} +85 < 70\\[/tex]
where, x is the number of weeks of exercise is necessary to lower the individual's resting heart rate below 70 beats per minute.
This cubic inequality can be solved by hit and trial method.
when x = 7.
[tex]-0.1x^{3} + 0.6x^{2} +85 < 70\\[/tex]
[tex]=-0.1*7^{3} + 0.6*7^{2} +85[/tex] = 80.1
80.1 > 70
Thus, x = 7 is not suitable.
when x = 8.
[tex]-0.1x^{3} + 0.6x^{2} +85 < 70\\[/tex]
[tex]=-0.1*8^{3} + 0.6*8^{2} +85[/tex] = 72.2
72.2 > 70
Thus, x = 8 is not suitable.
when x = 9.
[tex]-0.1x^{3} + 0.6x^{2} +85 < 70\\[/tex]
[tex]=-0.1*9^{3} + 0.6*9^{2} +85[/tex] = 60.7
60.7 < 70
Thus, x = 9 is suitable.
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