Answer:
The balloon will not reach 2,500 feet after 4 minutes.
Step-by-step explanation:
The equation of the line in the point-slope form is
[tex]y-y_1=m(x-x_1)[/tex]
A hot air balloon in flight begins to ascend at a steady rate of 120 feet per minute, then the slope is
[tex]m=120[/tex]
After [tex]x_1=1.5[/tex] minutes, the balloon is at an altitude of [tex]y_1=2,150[/tex] feet. This means, the line passes through the point (1.5, 2,150).
Substitute the slope and point coordinates into the equation:
[tex]y-2,150=120(x-1.5)[/tex]
We know that after 3 minutes, the balloon is at an altitude of 2,330 feet. Check this:
[tex]2,330-2,150=180\\ \\120(3-1.5)=120\cdot 1.5=180\\ \\2,330-2,150=120(3-1.5)[/tex]
Now, find the height after 4 minutes:
[tex]y-2,150=120(4-1.5)\\ \\y=120\cdot 2.5+2,150=300+2,150=2,450[/tex]
Thus, the balloon will reach only 2,450 feet after 4 minutes.
