Respuesta :
Using a linear function, it is found that:
- The equation that has to be solved is: [tex]-4.8t + 13 = 1[/tex]
- It takes 2.5 seconds for the acorn to be 1 foot above the ground.
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A linear function modeling the height after t seconds has the following format:
[tex]h(t) = at + h(0)[/tex]
In which:
- a is the slope, which is the rate of change of the height.
- h(0) is the initial height.
- The acorn is falling from 13 feet, thus [tex]h(0) = 13[/tex]
- It descends at a rate of 4.8 feet every second, thus the slope is negative, that is, [tex]a = -4.8[/tex]
- The equation for the height after t seconds is:
[tex]h(t) = -4.8t + 13[/tex]
- The acorn is 1 foot above ground when: [tex]h(t) = 1[/tex]
Thus:
[tex]h(t) = -4.8t + 13[/tex]
[tex]1 = -4.8t + 13[/tex]
[tex]-4.8t + 13 = 1[/tex]
[tex]4.8t = 12[/tex]
[tex]t = \frac{12}{4.8}[/tex]
[tex]t = 2.5[/tex]
It takes 2.5 seconds for the acorn to be 1 foot above the ground.
A similar problem is given at https://brainly.com/question/22881900
