Exercise 64 Page 322

Let's first find the equation. Then we can determine the maximum heart rate to maintain in aerobic training for an 80-year-old.

Equation

Looking at the given table, we see that the change in the age and the change in the pulse rate is constant.

As we get 10 years older, the pulse rate decreases by 9 beats per minute. There is a constant rate of change. Rate of Change = - 9/10 Since linear functions have a constant rate of change, we can model this data with a linear function. We will write the equation in the slope-intercept form. We can find the slope by substituting two points in the Slope Formula. Let's use (20,175) and (30,166).

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 20,175) & ( 30,166)

m=166- 175/30- 20

SubTerms

Subtract terms

m=-9/10

MoveNegNumToFrac

Put minus sign in front of fraction

m=- 9/10

We can substitute m=- 910 in the slope-intercept form. y & = mx + b y & = -9/10x+ b Let's find b by substituting one of the points in the equation. We can take (40,157).

y=-9/10x+b

SubstituteII

x= 40, y= 157

157=- 9/10( 40)+b

▼

Solve for b

MoveRightFacToNum

a/c* b = a* b/c

157=-360/10+b

CalcQuot

Calculate quotient

157=-36+b

AddEqn

LHS+36=RHS+36

193=b

RearrangeEqn

Rearrange equation

b=193

We can now complete our equation. y=- 910x+ 193 Finally, we will write it in function notation by replacing y with f(x). f(x)=-9/10x+193

Maximum Heart Rate

To determine the maximum heart rate to maintain in aerobic training for an 80-year-old, we have to substitute x=80 in our equation. Let's do it!

f(x)=-9/10x+193

Substitute

x= 80

f( 80)=-9/10 ( 80)+193

▼

Evaluate right-hand side

Multiply

Multiply

f(80)=-720/10+193

CalcQuot

Calculate quotient

f(80)=-72+193

AddTerms

Add terms

f(80)=121

The maximum heart rate to maintain in aerobic training for an 80-year-old is 121 beats per minute.