h(t)=15t + 1200 is a function that models the motion of a mountain climber. h(t) is his height above sea level at time t in minutes.
1a) the coefficient on t is 15. what does it tell you about the motion of the mountain climber?
1b) what does it tell you about the graph of h(t)?
2) is it reasonable to say h(1000) = 16200? why or why not? yes but i don't know why. i just did the math and it fits.
can someone help me?
the 15 would be the number of units of height he would climb every minute
You don't say what units, but I would assume h(t) is in metres.
the graph would be increasing, that is, it would rise to the right.
h(1000) makes no physical sense even though you get a mathematical answer. It means that he was climbing constantly for 1000 minutes, and would have reached a height of 16200 m or 16.2 km.
Considering the fact that Mt Everest is about 8.8 km above sea level .....
1a) The coefficient on t, which is 15 in this case, tells you the rate of change of the mountain climber's height with respect to time. Since the coefficient is positive, it indicates that the climber's height is increasing over time.
1b) The coefficient of t, being positive, means that the graph of h(t) will have a positive slope. This translates to an upward trend, indicating that the mountain climber is ascending in height over time.
2) To determine if it is reasonable to say h(1000) = 16200, we need to substitute t = 1000 into the given function and evaluate it. Plugging in 1000 for t, we get:
h(1000) = 15(1000) + 1200
= 15000 + 1200
= 16200
Since the calculated value matches the given value, it is indeed reasonable to say h(1000) = 16200. In this case, you have done the calculation correctly, and the result fits the given information.