Rates of change (1 Viewer)

[kpad5991]

1. The rate R litres per second at which water is flowing out of a tank is given by R = 7 + 6t -t^2 at time t seconds.

i) Calculate the total volume of water released from the tank in the first 3 seconds.

ii) Explain why this model only applied for the first 7 seconds.

2. The rate of growth of a plant is given by dh/dt = 1/(2t+1)^0.5 where h is the height in metres and t is the time in years. If a 4 year old plant is 2 metres high calculate the height of a 12 year old plant.

 

[Papercutter]

For Q1, I changed R to "dR/dt" because it concerns the rate of water flowing out over time. Integrating this with the bounds being 0 and 3 gives you the total volume of water released when 0 < t < 3. For Q1 ii), if you let dR/dt = 0 and then solve for t, you get t=7 or t=-1, but time cannot be negative, so t=7 is the only correct answer.

For Q2, it's just a simple matter of integrating dh/dt and using the given information (when t=4, h=2) to find the constant C. Then you can find the height of a 12 year old plant by subbing in t=12.