2.10 Logarithmic scaling and linearizing data Quiz

1. Taking $\ln$ of $y=ab^{x}$ gives...

• A. $\ln y=\ln a+b\ln x$
• B. $\ln y=\ln a+x\ln b$
• C. $\ln y=a+bx$
• D. $\ln y=x\ln(ab)$

2. A straight line of $\ln y$ against $\ln x$ has gradient 2.5. The model is...

• A. $y=ab^{2.5x}$
• B. $y=2.5x+k$
• C. $y=k\times2.5^{x}$
• D. $y=kx^{2.5}$

3. A quantity increases by a factor of 1000. By how much does $\log_{10}$ of the quantity increase?

• A. $1000$
• B. $10$
• C. $3$
• D. $1$

4. $\ln y$ against $\ln x$ has $r=0.12$. This suggests that...

• A. $y$ is not well modelled by a power function of $x$
• B. $y$ is exponential in $x$
• C. $n=0.12$
• D. $k=0.12$

5. $\ln y=1.2+0.5x$ for $y=ab^{x}$. Find $a$ and $b$.

• A. $a=1.2$, $b=0.5$
• B. $a=0.5$, $b=1.2$
• C. $a=3.32$, $b=1.65$
• D. $a=3.32$, $b=0.5$