17 0.84/1 points | Previous Answers WaneAC6 3.5.081 The following curve is a mod

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17 0.84/1 points | Previous Answers WaneAC6 3.5.081 The following curve is a model of a certain country's total prison population as a function of time in years (t-0 represents 1995). 1.65 1.55 1.5 1.45 z 1.35 0 2 3 4 5 6 7 89 10 Year (a) Which is correct? Over the period [5, 10] the instantaneous rate of change of N is increasing o Over the period [5, 10] the instantaneous rate of change of N is decreasing (b) Which is correct? The instantaneous rate of change of prison population at t = 4 was less than the average rate of change over the interval [0, 10]. O The instantaneous rate of change of prison population at t = 4 was greater than the average rate of change over the interval [0, 10] The instantaneous rate of change of prison population at t = 4 was approximately equal to the average rate of change over the interval [0, 10 (c) Which is correct? o Over the period [0, 10] the instantaneous rate of change of N is increasing, then decreasing Over the period [0, 10] the instantaneous rate of change of N is decreasing, then increasing Over the period [0, 10] the instantaneous rate of change of N is always increasing Over the period [0, 10] the instantaneous rate of change of N is always decreasing (d) According to the model, this country's total prison population was increasing fastest around what year? 1999 (e) Roughly estimate the instantaneous rate of change of N at t = 4 by using a balanced difference quotient with h = 1.5. (Round your answer to three decimal places.) 0.033 million prisoners per year Interpret the result. In 1999, this country's total number of prisoners was increasingat a rate of approximately 0.033 x prisoners per year

Explanation / Answer

(a) Over the period [5,10] the instantaneous rate of change of N is decreasing as it is evident that the slope of the curve is gradually decreasing.

(b) The instantaneous rate of change of prison population at t=4 was greater than the average rate of change over [0,10] as the slope of the curve at t=4 is more than the slope of the chord joining the points t=0 and t=10.

(c) It is evident from the slope of the curve that the slope is increasing first and then decreasing, hence the instantaneous rate of change of N is increasing and then decreasing.

(d) According to the model, total prison population was increasing fastest around t=4 as the slope of the curve is highest from t=3 to t=5.

(e) Prison population at t=3 and t=5 are (1.55-0.05/4) millions and (1.45+0.05/4) millions respectively.

Therefore, change of population trom t=3 to t=5 is 0.075 millions.

Hence, Instantaneous rate of change of N at t=4 is 0.075/2 millons/year=0.038 millions/year.

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