Question

A landscaper mows lawns for at least 3 hours but not more than 6 hours. the landscaper can mow 44,000 ft2 per hour. the function f(t)=44,000t represents the number of square feet the landscaper can mow in t hours. what is the practical range of the function?

Answer 1

Answer:
`132000 \le f(t) \le 264000`

Step-by-step explanation:

The domain is
`3 \le t \le 6` to represent the time values between 3 and 6 hours, including the endpoints. This represents the set of possible inputs to the function.

The function f(t) = 44000t is an increasing function. This means the smallest range value corresponds to the smallest domain value.

Plug in t = 3 to find that:

f(t) = 44000t

f(3) = 44000*3

f(3) = 132000

This says he mows 132,000 sq ft of lawn in 3 hours.

Now plug in the largest domain value to find the largest range value

f(t) = 44000t

f(6) = 44000*6

f(6) = 264000

He mows 264,000 sq ft of lawn in 6 hours.

The range is the set of f(t) values between 132,000 and 264,000

We can write that as
`132000 \le f(t) \le 264000`