Question

Doctors have two methods of calculating maximum heart rate. With the first method, maximum heart rate, y, in beats per minute is y = 220 − x, where x is the person's age. Maximum heart rate with the second method is shown in the table.

Age, x 20 30 40 50 60
Heart rate (bpm), y 194 187 180 173 166


Which method gives the greater maximum heart rate for a 90−year-old?

The method gives the greater heart rate.

Answer 1

The second method (table) gives the greater heart rate.

Explanation:

The given expression is

`y=220-x`

Where
`x` is age.

Now, for
`x=90`, we have

`y=220-90=130`

The equation gives 130 bpm for a 90-year-old patient.

Now, if we observe the given table, we would find a pattern there. The heart rate decreases by 7 while ages decreases by 10, so

For 60 y/o we have 166 bpm.

For 70 y/o we have 159 bpm.

For 80 y/o we have 152 bpm.

For 90 y/o we have 145 bpm.

If we compare, the second method (table) gives the greater heart rate.

Answer 2

The second method gives the greater heart rate.

Explanation:

In the second method, the age and heart rate(bpm) are in a linear relationship.

Therefore, the maximum heart rate for a 90-year-old person in the second method is = 194 - (194 - 187)7 = 145 bpm.

{Since, the maximum heart rate in the second method decreases in an A.P. having value at the age of 20 is 194 and it decreases by 7 bpm per 10 years}

Now, in the first method, the maximum heart rate for 90-year-old person is y = 220 - 90 = 130 bpm.

Therefore, the second method gives a greater heart rate. (Answer)