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Suppose an object is thrown upward with initial velocity of 32 feet per second from a height of 50 feet.
The height of the object t seconds after it is thrown is given by h(t) = - 161 + 32t + 50
Find the
average rate of change between t = 2 and t = 4. State what this means in context.

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Answer:

To find the average rate of change between t = 2 and t = 4, we need to calculate the difference in the height at these two time points and divide it by the difference in time.First, let's find the height at t = 2: h(2) = -161 + 32(2) + 50 h(2) = -161 + 64 + 50 h(2) = -161 + 114 h(2) = -47Next, let's find the height at t = 4: h(4) = -161 + 32(4) + 50 h(4) = -161 + 128 + 50 h(4) = -161 + 178 h(4) = 17Now, we can calculate the average rate of change: Average rate of change = (h(4) - h(2)) / (4 - 2) Average rate of change = (17 - (-47)) / (4 - 2) Average rate of change = (17 + 47) / 2 Average rate of change = 64 / 2 Average rate of change = 32The average rate of change between t = 2 and t = 4 is 32 feet per second. This means that, on average, the height of the object is changing by 32 feet per second during this time interval.

Step-by-step explanation:

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