The depth of water, d metres, in a reservoir in Kenya is modelled by a curve. At 6:00 am, a tangent to the curve passes through the points (4, 8) and (8, 6), where time is measured in hours after midnight.

What is the rate of change of depth at 6:00 am?

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Question

The depth of water, d metres, in a reservoir in Kenya is modelled by a curve. At 6:00 am, a tangent to the curve passes through the points (4, 8) and (8, 6), where time is measured in hours after midnight.

What is the rate of change of depth at 6:00 am?

Accepted Answer

−0.5 metres per hour — 5 metres per hour). Award 1 mark for correct calculation: gradient = (6 − 8) ÷ (8 − 4) = −2 ÷ 4 = −0.5. A is incorrect — this ignores the negative sign, which indicates the depth is decreasing. C is incorrect — this calculates run ÷ rise instead of rise ÷ run. D is incorrect — this inverts the fraction incorrectly.

Answer

−0.5 metres per hour

Answer

0.5 metres per hour

Answer

2 metres per hour

Answer

−2 metres per hour

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