The Baker formula estimates the maximum heart rate, in beats per minute, of a person who isa years old. The formula is shown below:b(a) = 200 -0.75aAt what age is the maximum heart rate 188 beats per minute?
Accepted Solution
A:
Answer:For a=16, the Maximum Heart Rate is 188 Beats Per Minute. Step-by-step explanation:To begin, we know that the formula:[tex]b(a)=200-0.75a[/tex] Eqn(1).is equivalent to a linear equation of algebraic form denoted as:[tex]y=k+mx[/tex] Eqn(2)as such that Eqns (1) and (2) relate as follow:[tex]y[/tex] ⇔ [tex]b(a)[/tex]: denoting our Dependent Variable, in this case Max. Heart Rate in Beats Per Minute[tex]x[/tex] ⇔ [tex]a[/tex]: is our Independent Variable, in this case the Age of the Person[tex]m[/tex] ⇔ [tex]0.75[/tex]: denoting the Rate of Change of the Age.[tex]k[/tex] ⇔ [tex]200[/tex]: denoting our Constant.Now in the question our value of [tex]b(a)[/tex] is given as 188 beats per minute, which by plugging in Eqn(1) gives:[tex]200-0.75a=188[/tex]from which we can solve to obtain the value of [tex]a[/tex] as follow:[tex]-0.75a=188-200[/tex] Gather similar terms on each side[tex]-0.75a=-12\\[/tex] Simplify[tex]a=\frac{-12}{-0.75}[/tex] Solve for [tex]a[/tex][tex]a=16[/tex]Which tells us that at the Age of 16, the Max. Heart Rate is 188 Beats Per Minute.