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The table shows a hot air balloon's height h , in feet, during a descent at various times t , in seconds.
Part A: Use the table's first two ordered pairs to find the hot air balloon's rate of change.

Part B: Is the rate of change constant? Explain.

Part C: What was the hot air balloon's height at the time the descent began?

Part D: Write , as a linear function of
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The table shows a hot air balloons height h in feet during a descent at various times t in seconds Part A Use the tables first two ordered pairs to find the hot class=

Respuesta :

Using a linear function, we have that:

A. The rate of change is of -12 feet per second.

B. The rate of change is constant.

C. The initial height is of 1210 feet.

D. The linear function is: h(t) = -12t + 1210.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

From the table, when x changes by 5 seconds, the height decreases by 60 feet, hence the slope is given by:

m = -60/5 = -12 feet per second.

Hence the function is:

h(t) = -12t + b.

When t = 5, h(t) = 1150, hence we use this to find the initial height.

h(t) = -12t + b.

1150 = -12(5) + b.

b = 1210.

Hence the linear function is:

h(t) = -12t + 1210.

More can be learned about linear functions at https://brainly.com/question/24808124

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