Question

your work.

1. a hot air balloon was at a height of 60 feet above

the ground when it began to ascend. the balloon
climbed at a rate of 15 feet per minute.

a. make a table that shows the height of the hot
air balloon after climbing for 1, 2, 3, and
4 minutes.

b. let t represent the time in minutes since the
balloon began climbing. write an algebraic
equation for a sequence that can be used to
find the height, h, of the balloon after t
minutes.

c. use your equation from part b to find the
height, in feet, of the hot air balloon after
climbing for 8 minutes.

Explanation:

Part a

Step1: Determine height formula

The initial height is 60 feet, and the rate of climb is 15 feet per minute. So the height \( h \) after \( t \) minutes is \( h = 60 + 15t \).

Step2: Calculate for \( t = 1 \)

Substitute \( t = 1 \) into the formula: \( h = 60 + 15(1) = 75 \) feet.

Step3: Calculate for \( t = 2 \)

Substitute \( t = 2 \): \( h = 60 + 15(2) = 60 + 30 = 90 \) feet.

Step4: Calculate for \( t = 3 \)

Substitute \( t = 3 \): \( h = 60 + 15(3) = 60 + 45 = 105 \) feet.

Step5: Calculate for \( t = 4 \)

Substitute \( t = 4 \): \( h = 60 + 15(4) = 60 + 60 = 120 \) feet.

Step6: Create the table

Time (minutes)	Height (feet)
2	90
3	105
4	120

Part b

Step1: Identify initial value and rate

Initial height (\( b \)) is 60 feet, rate of change (\( m \)) is 15 feet per minute.

Step2: Use linear equation form

The linear equation for height \( h \) in terms of time \( t \) is \( h = mt + b \). Substituting \( m = 15 \) and \( b = 60 \), we get \( h = 15t + 60 \).

Part c

Step1: Use the equation from part b

The equation is \( h = 15t + 60 \).

Step2: Substitute \( t = 8 \)

Substitute \( t = 8 \) into the equation: \( h = 15(8) + 60 \).

Step3: Calculate the value

First, \( 15(8) = 120 \), then \( 120 + 60 = 180 \).

Answer:

s:
a. The table is as shown above.
b. The equation is \( \boldsymbol{h = 15t + 60} \).
c. The height after 8 minutes is \(\boldsymbol{180}\) feet.