Logarithmic graphs and modelling growth and decay Quiz

1. A graph of $\log_{10}y$ against $\log_{10}x$ is a straight line with gradient $3$ and intercept $1$. Which relationship does it show?

• A. $y=3x^{10}$
• B. $y=10x^{3}$
• C. $y=x^{3}+10$
• D. $y=10^{3}x$

2. For $y=5\times2^{x}$, what is the gradient of $\log_{10}y$ plotted against $x$?

• A. $2$
• B. $0.301$
• C. $5$
• D. $0.699$

3. $P=200e^{-0.05t}$. Find $P$ when $t=10$, to 3 significant figures.

• A. $300$
• B. $150$
• C. $200$
• D. $121$

4. For $N=Ae^{-kt}$ with $A>0$ and $k>0$, what happens to $N$ as $t$ becomes very large?

• A. $N$ tends to $A$
• B. $N$ tends to $0$
• C. $N$ increases without limit
• D. $N$ becomes negative

5. A radioactive sample follows $A=100e^{-0.2t}$, with $t$ in years. Find its half-life, to 3 significant figures.

• A. $5.00$ years
• B. $2.50$ years
• C. $3.47$ years
• D. $0.347$ years