Question

A hot air balloon descends to the ground. The function a(t) = 210 - 15t represents the altitude of the balloon in feet as a function of time t in seconds. How long will it take for the balloon to reach an altitude of 90 feet? A) 8 seconds B) 7 seconds C) 6 seconds D) 5 seconds

Answer 1

The hot air balloon will reach an altitude of 90 feet in 8 seconds. The function a(t) = 210 - 15t is solved for t when a(t) equals 90. Upon solving, t equals 8, therefore the correct answer is 8 seconds.

Step-by-step explanation:

The question asks how long it will take for a hot air balloon to reach an altitude of 90 feet. The given function is a linear equation that represents the balloon's altitude over time: a(t) = 210 - 15t. To find out when the balloon will be at 90 feet, we simply need to solve the equation for t when a(t) is 90.

Setting a(t) to 90, we have the equation: 90 = 210 - 15t.

Rearranging for t gives us (-90 + 210) / 15 = t. Solving for t, we get t = 8.

Therefore, the balloon will reach an altitude of 90 feet in 8 seconds.

So, the correct answer is A) 8 seconds.

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