Exponents and exponential growth/decay Knowledge-Based Download PDF

Questions

1. 1.

   For an exponential decay model given by $Q(t) = Q_0 \cdot 8^{-t/6}$, where $t$ is measured in minutes, what is the value of the ratio $\frac{Q(t+2)}{Q(t)}$?

   • A) $\frac{1}{8}$
   • B) $\frac{1}{6}$
   • C) $\frac{1}{4}$
   • D) $\frac{1}{2}$
2. 2.

   An exponential growth function is given by $f(x) = C \cdot a^x$, where $C$ and $a$ are positive constants. If $f(2) = 18$ and $f(5) = 486$, what is the value of $f(0)$?

   • A) 6
   • B) 4
   • C) 3
   • D) 2
3. 3.

   A certain medication decreases in the bloodstream at a rate of 20% per hour. If an initial dose of 250 mg is administered, how many milligrams of the medication remain in the bloodstream after 3 hours?

   • A) 100 mg
   • B) 128 mg
   • C) 150 mg
   • D) 160 mg
4. 4.

   A culture of bacteria triples in population every 4 hours. If the culture initially contains 250 bacteria, what will the population be after 12 hours?

   • A) 2250
   • B) 3000
   • C) 6750
   • D) 20250
5. 5.

   A radioactive sample has an initial mass of 320 grams and a half-life of 15 days. What is the remaining mass of the sample after 60 days?

   • A) 80 grams
   • B) 40 grams
   • C) 10 grams
   • D) 20 grams