A student in Jamaica investigates the rate at which sugar cane juice ferments by measuring the volume of carbon dioxide produced over time. The graph of volume against time is a smooth curve. To estimate the rate of fermentation at exactly 30 minutes, the student should:

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Question

A student in Jamaica investigates the rate at which sugar cane juice ferments by measuring the volume of carbon dioxide produced over time. The graph of volume against time is a smooth curve. To estimate the rate of fermentation at exactly 30 minutes, the student should:

Accepted Answer

Draw a tangent to the curve at 30 minutes and calculate its gradient — Award 1 mark for recognizing that the gradient of the tangent at a point gives the instantaneous rate at that exact time. A is incorrect because a chord gives an average rate over an interval, not the rate at a specific point. C is incorrect because the average gradient does not give the rate at a specific time. D is incorrect because this gives an average rate over 10 minutes, not the instantaneous rate at 30 minutes.

Answer

Draw a tangent to the curve at 30 minutes and calculate its gradient

Answer

Find the average gradient over the entire curve

Answer

Calculate the difference in volume between 25 and 35 minutes

Answer

Calculate the gradient of the chord joining the origin to the point at 30 minutes

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