Question

The Baker formula estimates the maximum heart rate, in beats per minute, of a person who is
a years old. The formula is shown below:
b(a) = 200 -0.75a
At what age is the maximum heart rate 188 beats per minute?​

Answer 1

Answer:

For a=16, the Maximum Heart Rate is 188 Beats Per Minute.

Step-by-step explanation:

To begin, we know that the formula:

$b(a)=200-0.75a$    Eqn(1).

is equivalent to a linear equation of algebraic form denoted as:

$y=k+mx$                  Eqn(2)

as such that  Eqns (1) and (2) relate as follow:

$y$ ⇔ $b(a)$: denoting our Dependent Variable, in this case Max. Heart Rate in Beats Per Minute

$x$ ⇔ $a$: is our Independent Variable, in this case the Age of the Person

$m$ ⇔ $0.75$: denoting the Rate of Change of the Age.

$k$ ⇔ $200$: denoting our Constant.

Now in the question our value of $b(a)$ is given as 188 beats per minute, which by plugging in Eqn(1) gives:

$200-0.75a=188$

from which we can solve to obtain the value of $a$ as follow:

$-0.75a=188-200$          Gather similar terms on each side

$-0.75a=-12$                   Simplify

$a=\frac{-12}{-0.75}$                           Solve for $a$

$a=16$

Which tells us that at the Age of 16, the Max. Heart Rate is 188 Beats Per Minute.