2.9 Further modelling functions Quiz

1. A substance has half-life 5 days. What fraction remains after 15 days?

• A. $\frac12$
• B. $\frac14$
• C. $\frac18$
• D. $\frac1{15}$

2. What is the carrying capacity of $f(x)=\frac{500}{1+9e^{-0.4x}}$?

• A. $500$
• B. $50$
• C. $9$
• D. $0.4$

3. In radians, what is the period of $y=3\sin(2(x-1))+4$?

• A. $2\pi$
• B. $2$
• C. $3$
• D. $\pi$

4. For which $a$ is $f(x)=1+x$ for $x<2$ and $f(x)=ax^2+x$ for $x\ge2$ continuous at $x=2$?

• A. $0.5$
• B. $0.25$
• C. $1$
• D. $4$

5. Which statement is true for $f(x)=a+b\ln x$ with $b>0$?

• A. it is defined for all real $x$
• B. it has a horizontal asymptote $y=a$
• C. it increases without bound, but ever more slowly
• D. it is periodic