Find the nth term of each of the sequences. (a) 16, 19, 22, 25, 28, ... (b) 1,3,9,27,81,...
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So for this, since the rate is linear we will be using the slope-intercept form, which is y=mx+b (m = slope/rate of change, b = y-intercept)
Since the rate of change "descends 150 ft per min", the m variable is -150.
The y-intercept is, in this case, the height of the balloon at 0 mins, or the starting height. Since the balloon "is at a height of 2250 ft", the b variable is 2250.
Putting our equation together, its y = -150x + 2250.
Since time is our independent variable, plug in 6, 8, and 10 mins into the x variable to solve for their heights:
In context, after 6 minutes the balloon is at 1,350 ft, after 8 minutes the balloon is at 1,050 ft, and after 10 minutes the balloon is at 750 ft.