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Answer :
To find the practical range of the function [tex]\( f(t) = 44,000t \)[/tex], which represents the number of square feet a landscaper can mow in [tex]\( t \)[/tex] hours, let's go through the steps:
1. Identify the range for [tex]\( t \)[/tex]: The landscaper mows lawns for at least 3 hours and no more than 6 hours. Therefore, the possible values for [tex]\( t \)[/tex] are 3, 4, 5, and 6.
2. Calculate the corresponding output values of the function [tex]\( f(t) \)[/tex]:
- For [tex]\( t = 3 \)[/tex], the area mowed is:
[tex]\[
f(3) = 44,000 \times 3 = 132,000
\][/tex]
- For [tex]\( t = 4 \)[/tex], the area mowed is:
[tex]\[
f(4) = 44,000 \times 4 = 176,000
\][/tex]
- For [tex]\( t = 5 \)[/tex], the area mowed is:
[tex]\[
f(5) = 44,000 \times 5 = 220,000
\][/tex]
- For [tex]\( t = 6 \)[/tex], the area mowed is:
[tex]\[
f(6) = 44,000 \times 6 = 264,000
\][/tex]
3. Determine the practical range of the function: The practical range includes all possible outputs from the function based on the given constraints for [tex]\( t \)[/tex]. Therefore, the range covers:
[tex]\[
132,000, 176,000, 220,000, \text{ and } 264,000
\][/tex]
By listing these possible areas that can be mowed, we find that the practical range of the function is:
- All multiples of 44,000 between 132,000 and 264,000, inclusive.
This means the correct answer is:
"all multiples of 44,000 between 132,000 and 264,000, inclusive."
1. Identify the range for [tex]\( t \)[/tex]: The landscaper mows lawns for at least 3 hours and no more than 6 hours. Therefore, the possible values for [tex]\( t \)[/tex] are 3, 4, 5, and 6.
2. Calculate the corresponding output values of the function [tex]\( f(t) \)[/tex]:
- For [tex]\( t = 3 \)[/tex], the area mowed is:
[tex]\[
f(3) = 44,000 \times 3 = 132,000
\][/tex]
- For [tex]\( t = 4 \)[/tex], the area mowed is:
[tex]\[
f(4) = 44,000 \times 4 = 176,000
\][/tex]
- For [tex]\( t = 5 \)[/tex], the area mowed is:
[tex]\[
f(5) = 44,000 \times 5 = 220,000
\][/tex]
- For [tex]\( t = 6 \)[/tex], the area mowed is:
[tex]\[
f(6) = 44,000 \times 6 = 264,000
\][/tex]
3. Determine the practical range of the function: The practical range includes all possible outputs from the function based on the given constraints for [tex]\( t \)[/tex]. Therefore, the range covers:
[tex]\[
132,000, 176,000, 220,000, \text{ and } 264,000
\][/tex]
By listing these possible areas that can be mowed, we find that the practical range of the function is:
- All multiples of 44,000 between 132,000 and 264,000, inclusive.
This means the correct answer is:
"all multiples of 44,000 between 132,000 and 264,000, inclusive."
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