Exponential growth and decay models Quiz

1. A quantity is modelled by $N=500e^{0.2t}$. What is its initial value?

• A. $0.2$
• B. $100$
• C. $500$
• D. $1$

2. $P=200e^{-0.1t}$. Find the time taken for $P$ to halve.

• A. $6.93$
• B. $0.693$
• C. $10$
• D. $13.9$

3. $N=40e^{0.5t}$. Find $\frac{dN}{dt}$ when $t=2$, to 3 s.f.

• A. $108.7$
• B. $20$
• C. $40$
• D. $54.4$

4. A drink cools according to $T=15+60e^{-0.05t}$. What temperature does the model predict in the long term?

• A. $0^\circ$C
• B. $15^\circ$C
• C. $60^\circ$C
• D. $75^\circ$C

5. $P=Ae^{kt}$ with $P=100$ at $t=0$ and $P=150$ at $t=2$. Find $k$ to 3 s.f.

• A. $0.405$
• B. $0.25$
• C. $0.203$
• D. $0.5$