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4 years ago

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A hot-air balloon descends from a height of 2000 feet for 40 seconds. The function models the height of the hot-air balloon duri

ng this descent, where t is the amount of time since the descent began. What is the practical domain of the function in this situation? What is the practical range of the function in this situation?

1 answer:

Zielflug [23.3K]4 years ago

8 0

Answer:

The domain is all real values greater than or equal to 0 seconds and less than or equal to 40 seconds

The range is all real values greater than or equal to 0 feet and less than or equal to 2,000 feet

Step-by-step explanation:

Let

t ----> is the amount of time since the descent began

f(t) ---> is the height of a hot-air balloon descends

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the unit rate or slope of the linear equation

b is the y-intercept or initial value

In this problem we have that

The slope or unit rate is equal to

$m=-\frac{2,000}{40}=-50\ feet\ per\ second$ ---> is negative because is a decreasing function

The y-intercept or initial value is equal to

$b=2,000\ ft$

substitute

$f(t)=-50t+2,000$

The domain is the interval -----> [0,40]

$0\leq t\leq 40$

All real values greater than or equal to 0 seconds and less than or equal to 40 seconds

The range is the interval ----> [0,2,000]

$0\leq f(t)\leq 2,000$

All real values greater than or equal to 0 feet and less than or equal to 2,000 feet

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