Aperson’s theoretical maximum heart rate (in heartbeats per minute) is 220 - x where x is the person’s age in years (20 ≤ x ≤ 65). when a person exercises, it is recommended that the person strive for a heart rate that is at least 50% of the maximum and at most 75% of the maximum. write a system of linear inequalities that describes the given information.

Let f(x) represents the heart beat of the person.

Now, we have been given that person’s theoretical maximum heart rate is given by  220 - x.

Also, we have been given that person strive for a heart rate that is at least 50% of the maximum. At least means greater than equal to.

Thus, we have

Also, we have been given that person strive for a heart rate that is at most 75% of the maximum. At most means less than equal to.

Therefore, the system of inequality is given by

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

d is the only accurate one

step-by-step explanation: