Answer to Question #186945 in Math for bryan

Question

a water tanker used a garden centre is filled by the rain and emptied as the water is used to water plants. the volume of water in the tank over a particular week is modelled by the equation v=30+6t-t^2 for 0≤t≤7, where v is the volume in litres and t is the time in days from the start of the week.

1- find the rate, in litre per day, at which the volume of water is increasing after 2 days.

2- find the maximum volume of water in the tank during the week.

Answer 1

1.

$$\dfrac{dv}{dt}=(30+6t-t^2)'=6-2t$$

$$\dfrac{dv}{dt}(2)=6-2(2)=2(l/day)$$

The volume of water is increasing with rate of 2 litres per day after 2 days.

2.

$$\dfrac{dv}{dt}=0=>6-2t=0=>t=3$$

$v(0)=30$

$v(7)=30+6(7)-(7)^2=23$

$v(3)=30+6(3)-(3)^2=39$

The maximum volume of water in the tank during the week is 39 litres after 3 days.