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

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

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=(-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.