<p>Five hundred litres of salt solution is kept in a huge tank.</p>
<p>A man turns on a tap to allow salt solution containing $250$g of salt per litre of water to be poured into this tank at a rate of $4$ litres/min. At the same time, the well-stirred solution is withdrawn from the tank at a rate of $4$ litres/min.</p>
<p>It is known that there is $50$kg of salt dissolved in the salt solution before the tap is turned on.</p>
<p>Let $y$ kg be the amount of salt in the tank at time $t$ minutes after the tap is turned on.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Show that $y$ satisfies the following differential equation</div><div class="list-item-paragraph" style="text-align: center">$\frac{\mathrm{d}y}{\mathrm{d}t}=1-\frac{y}{125}$</div><p style="text-align: right;">[3]</p></li><li><div class="list-item-paragraph">Find $y$ in terms of $t$.</div><p style="text-align: right;">[4]</p></li><li><div class="list-item-paragraph">Find the amount of salt in the tank when $t=20$.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">State what happens to $y$ for large values of $t$.</div><p style="text-align: right;">[1]</p></li></ol>

Five hundred litres of salt solution is kept in a huge tank.

A man turns on a tap to allow salt solution containing $250$g of salt per litre of water to be poured into this tank at a rate of $4$ litres/min. At the same time, the well-stirred solution is withdrawn from the tank at a rate of $4$ litres/min.

It is known that there is $50$kg of salt dissolved in the salt solution before the tap is turned on.

Let $y$ kg be the amount of salt in the tank at time $t$ minutes after the tap is turned on.

Show that $y$ satisfies the following differential equation

$\frac{\mathrm{d}y}{\mathrm{d}t}=1-\frac{y}{125}$

Find the amount of salt in the tank when $t=20$.

State what happens to $y$ for large values of $t$.

Differential Equations - General

Differential Equations

International Baccalaureate Higher Level Mathematics

2015 SRJC BT2 P1 Q10

2015 SRJC BT2 P1 Q10

Video Solution:

Solution:

Handwritten & Typed Solutions