Question

1) El ritmo cardíaco de un gato ( en latidos por minuto) es función lineal de su temperatura corporal (en grados Celsius). En condiciones normales un gato con 37°C tiene un ritmo cardíaco de 200 pulsaciones por minuto y de 150 si su temperatura es de 32°C.

Answer 1

`y=10x-170`

Explanation:

This problem can be modeled by a linear function, where we have two points (37°C, 200) and (32°C, 150).

Notice that the temperature is the independent variable, because the heartbeat of the cat won't change the temperature, it works in the opposite way.

First, let's find the constant ratio of change.

`m=(150-200)/(32-37)=(-50)/(-5)=10`

This means the hearbeat of the car changes 10 pulses per minute each 1 celsius degree.

Now, we use the point slope formula to find the equation

`y-y_(1) =m(x-x_(1) )\\y-150=10(x-32)\\y=10x-320+150\\y=10x-170`

Theerefore, the function that represents this situation is

`y=10x-170`

Where
`x` represents temperature and
`y` represents hearbeats.