Exponential growth and decay Quiz

1. A population is modelled by $P=200\mathrm{e}^{0.03t}$. Find $P$ when $t=20$, to the nearest whole number.

• A. $120$
• B. $364$
• C. $600$
• D. $3.6$

2. A quantity decays as $N=500\mathrm{e}^{-0.2t}$. Find the time at which $N=100$, to 3 s.f.

• A. $2.5$
• B. $25$
• C. $0.0805$
• D. $8.05$

3. A radioactive isotope has $M=M_0\mathrm{e}^{-0.1t}$, with $t$ in years. What is its half-life?

• A. $6.93$ years
• B. $5$ years
• C. $0.693$ years
• D. $10$ years

4. Interest of 5% a year is compounded continuously. What is the equivalent annual rate to 3 s.f.?

• A. $5.00\%$
• B. $5.13\%$
• C. $4.88\%$
• D. $0.513\%$

5. Which is a valid limitation of $P=P_0\mathrm{e}^{kt}$ as a model of an animal population?

• A. It predicts a decreasing population
• B. It cannot be used with $t=0$
• C. It predicts that the population grows without limit
• D. It requires $k$ to be negative