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Answer :
To determine the practical range of the function [tex]\( f(t) = 44,000t \)[/tex], where [tex]\( t \)[/tex] represents the number of hours, we need to consider the time restrictions provided: the landscaper works for at least 3 hours and at most 6 hours.
1. Calculate the Minimum Mowing Area:
- The minimum time [tex]\( t \)[/tex] is 3 hours.
- Substitute [tex]\( t = 3 \)[/tex] into the function:
[tex]\[
f(3) = 44,000 \times 3 = 132,000 \text{ square feet}
\][/tex]
2. Calculate the Maximum Mowing Area:
- The maximum time [tex]\( t \)[/tex] is 6 hours.
- Substitute [tex]\( t = 6 \)[/tex] into the function:
[tex]\[
f(6) = 44,000 \times 6 = 264,000 \text{ square feet}
\][/tex]
3. Determine the Practical Range:
- The landscaper can mow any area between and including these two values.
- Additionally, since the function represents mowing at a constant rate of 44,000 square feet per hour, we see that the possible values must be multiples of 44,000 within the given bounds.
- Therefore, the practical range of the number of square feet the landscaper can mow is:
[tex]\[
132,000, 176,000, 220,000, 264,000
\][/tex]
- This corresponds to mowing for 3, 4, 5, and 6 hours respectively.
Thus, the practical range of the function is all multiples of 44,000 between 132,000 and 264,000, inclusive.
1. Calculate the Minimum Mowing Area:
- The minimum time [tex]\( t \)[/tex] is 3 hours.
- Substitute [tex]\( t = 3 \)[/tex] into the function:
[tex]\[
f(3) = 44,000 \times 3 = 132,000 \text{ square feet}
\][/tex]
2. Calculate the Maximum Mowing Area:
- The maximum time [tex]\( t \)[/tex] is 6 hours.
- Substitute [tex]\( t = 6 \)[/tex] into the function:
[tex]\[
f(6) = 44,000 \times 6 = 264,000 \text{ square feet}
\][/tex]
3. Determine the Practical Range:
- The landscaper can mow any area between and including these two values.
- Additionally, since the function represents mowing at a constant rate of 44,000 square feet per hour, we see that the possible values must be multiples of 44,000 within the given bounds.
- Therefore, the practical range of the number of square feet the landscaper can mow is:
[tex]\[
132,000, 176,000, 220,000, 264,000
\][/tex]
- This corresponds to mowing for 3, 4, 5, and 6 hours respectively.
Thus, the practical range of the function is all multiples of 44,000 between 132,000 and 264,000, inclusive.
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