Mathematical Methods · Unit 2 · Introduction to differential calculus · Rates of change and the concept of derivatives
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A spherical balloon is being inflated so that its radius \(r\) (in centimetres) is increasing according to the function \(r(t) = 3t^2 + 2t\), where \(t\) is the time in seconds. Determine the instantaneous rate of change of the radius with respect to time when \(t = 4\) seconds.
A cylindrical water tank is being drained. The volume of water remaining in the tank after \( t \) seconds is given by \( V(t) = 450 - 6t^2 \) litres, where \( 0 \leq t \leq 8 \). Determine the instantaneous rate at which the volume of water is changing when \( t = 5 \) seconds.
A substance is being heated such that its temperature T in °C after t minutes is given by the function T = 15 + 4t - 0.3t². The instantaneous rate of change of temperature at t = 5 minutes is 1 °C per minute. Which statement correctly interprets this value?