The number of tons of paper waiting to be recycled at a 24 h recycling plant can be modelled by the equation P(t) where t is the time, in hours, and P(t) is the number of tons waiting to be recycled. a) Use the equation to estimate the instantaneous rate of change in tons of paper waiting to be recycled when this rate is at its maximum. To make = 0.5 sin + 4, your estimate, use each of the following centred intervals: i) Ih before to I h after the time when the instantaneous rate of change is at its maximum ii) 0.5 h before to 0.5 h after the time when the instantaneous rate of change is at its maximum iii) 0.25 h before to 0.25 h after the time when the instantaneous rate of change is at its maximum b) Which estimate is the most accurate? What is the relationship between the size of the interval and the accuracy of the estimate?

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