3) [20 pts] A hospital is considering a new magnetic resonance imaging (MRI) machine. The new...

 

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3) [20 pts] A hospital is considering a new magnetic resonance imaging (MRI) machine. The new machine provides substantial initial savings, with the savings declining with time t (in years) according to the rate-of-savings function, S'(t) = 100-t² where S'(t) is in thousands of dollars per year (black curve on graph). At the same time, the cost of operating the new machine increases with time t (in years), according to the rate-of-cost function, C'(t) = t² +¹t where C'(t) is in thousands of dollars per year (red curve). 14 3 (6.64) a) [12 points] Find the area between the graphs of S' (t) and C (t) for 0 ≤ t ≤ 6. Round to the nearest thousand. b) [4 pts] What does the area between the graphs of S'(t) and C'(t) over the interval 0≤t≤ 6 represent? Explain in terms of the answer you got in part (a). c) [4 pts] Explain what happens after the 6-year period, that is explain the shaded area between the two curves after t> 6? 3) [20 pts] A hospital is considering a new magnetic resonance imaging (MRI) machine. The new machine provides substantial initial savings, with the savings declining with time t (in years) according to the rate-of-savings function, S'(t) = 100-t² where S'(t) is in thousands of dollars per year (black curve on graph). At the same time, the cost of operating the new machine increases with time t (in years), according to the rate-of-cost function, C'(t) = t² +¹t where C'(t) is in thousands of dollars per year (red curve). 14 3 (6.64) a) [12 points] Find the area between the graphs of S' (t) and C (t) for 0 ≤ t ≤ 6. Round to the nearest thousand. b) [4 pts] What does the area between the graphs of S'(t) and C'(t) over the interval 0≤t≤ 6 represent? Explain in terms of the answer you got in part (a). c) [4 pts] Explain what happens after the 6-year period, that is explain the shaded area between the two curves after t> 6?

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Area fb fort dy dz a Area Z 5 100 100 14 t dt 16 1001 d... View the full answer