Year 11 Maths - Methods Rates of Change

Instantaneous Rate of Change

ACCOUNT REQUIRED

Unlock all 5 questions & worked solutions

You're viewing a free preview. Create an account to access the complete question set, step-by-step solutions, and progress tracking.

All Questions

Access the full question set for every topic.

Worked Solutions

Step-by-step explanations for every answer.

Track Progress

Mark questions right or wrong and monitor your growth.

It's Free

No credit card required - sign up in under a minute.

Questions

Question 1

28806

The population \(P\) million of bacteria after \(t\) minutes is give by \(P = 4 \times {2^t}\) as illustrated in the graph. Estimate the instantaneous rate of change of \(P\) when \(x = 1\)

Answer

\(5.5~\text{million/min} \)

Worked Solution

\begin{align}
&\text{Let the tangent line be }\varphi(t)\\
&\varphi(1)=8 \text{ and } \varphi(0)= 2.5\\
&\begin{aligned}
\text{Instantaneous rate }&= \frac{\varphi(1)-\varphi(0)}{1-0}\\
&= \frac{8-2.5}{1} \\
&= 5.5 \mathrm{~millon} / \mathrm{min}
\end{aligned}
\end{align}

📚 Want More Questions?

There are 4 more questions available. Create your free account to access the complete question set with detailed solutions.

Get Full Access Already Have Account?