Question

Two years ago, doctors found that a benign tumor is growing in a patient’s brain. Though...

Two years ago, doctors found that a benign tumor is growing in a patient’s brain. Though it is benign, they have been monitoring its’ growth each year. The width of the tumor is given by the function P(t) where P is measured in mm, and t is measured in years since the tumor first formed. We know that P(2) = 2 and P' (2) = 1.5

1. What are the units of P' (t)?

2. Give a physical interpretation of the fact that P' (2) = 1.5 by writing out a sentence describing it.

3. Using P' (2), estimate how large the tumor will be in the middle of the third year P(3.5), and explain how you used Calculus to arrive at this answer.

4. Using P' (2), estimate the size of the tumor during the previous year P(1.2), and explain how you used Calculus to arrive at this answer.

5. Using P' (2), estimate P(0), and discuss whether or not your estimate is reasonable. (Think about what this should be based on the context of the problem, then compare that with the approximation you get using calculus)

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