Question

make connections the height h of a balloon, in feet, t seconds after it is released is given by the function h(t)=2t + 6.
a. what is the value of h(20), and what does it mean in the context of the situation?
h(20)=
the height of the balloon seconds after it is released is feet.
b. explain how to use the function to find the height of the balloon 2 minutes after it is released.
2 minutes is seconds, so calculate the value of the function by substituting t = in the equation.
the height of the balloon 2 minutes after it is released is feet.
c. what is the height of the balloon just before it is released? how do you know?
feet
t = before the balloon is released, and h()=

Explanation:

Step1: Substitute t = 20 into the function

$h(20)=2\times20 + 6$
$h(20)=40+6=46$
This means the height of the balloon 20 seconds after it is released is 46 feet.

Step2: Convert 2 minutes to seconds

Since 1 minute = 60 seconds, 2 minutes = 2×60 = 120 seconds. Then substitute t = 120 into the function.
$h(120)=2\times120+6=240 + 6=246$

Step3: Find the height before release

Before the balloon is released, t = 0. Substitute t = 0 into the function.
$h(0)=2\times0+6=6$

Answer:

a. h(20) = 46; The height of the balloon 20 seconds after it is released is 46 feet.
b. 2 minutes is 120 seconds, so calculate the value of the function by substituting t = 120 in the equation. The height of the balloon 2 minutes after it is released is 246 feet.
c. 6 feet; t = 0 before the balloon is released, and h(0)=6.