2003 HCI P2 Q2
Liquid is poured into a container at a constant rate of $30$cm$^{3}$s$^{-1}$ and leaks out at a rate which is proportional to the volume of liquid in the container. At time $t$ seconds, the volume of the water in the container is $V$cm$^{3}$. When the volume reaches $450$cm$^{3}$, it decreases at a rate of $30$cm$^{3}$s$^{-1}$ .
Show that $-15\frac{\text{d}V}{\text{d}t}=2V-450$.
[2]
It is given that $V=1000$cm$^{3}$ when $t=0$.
(i)
Show that $V=A{{e}^{\alpha \,t}}+B$, where $\alpha $, $A$ and $B$ are constants to be determined.
[4]
(ii)
Sketch the graph of $V$ against $t$.
[1]
Suggested Video Solutions
Share with your friends!
Continue reading
Introducing Our Sec 1 Assessment Book: From Concepts to Confidence
Welcome to Tim Gan Math Learning Centre, where we have been dedicated to nurturing mathematical excellence since our establishment in 2017. At our centre, we are committed to providing quality
Entangled in the Web: Managing Online Entertainment, Internet Addiction, and Academic Achievement in Math
In today’s digital age, the internet has seamlessly woven itself into the fabric of our daily lives, becoming an indispensable tool for communication, information, and, notably, entertainment. The allure of
Goal Setting and Progress Tracking for Math Students: A Comprehensive Guide
In the pursuit of academic success, setting and achieving goals play a pivotal role, particularly in disciplines like mathematics. Effective goal setting not only provides students with a roadmap for