Checkpoint: Applications of Exponents and Logs Solution

A biologist is studying a strain of bacteria that triples $(r = 3)$ every hour. If she starts with a culture containing 100 bacteria, how long will it take for 24,000 bacteria to be present? Round to the nearest quarter of an hour, t, using the formula: $Q (t) = Q_{0} {(r)}^{t}$

$Q_{0} = 100 r = 3 (triples) Q (t) = 24 000$

$24000 = 100 {(3)}^{t} 240 = 3^{t} \ln 240 = t \ln 3 t = \frac{\ln 240}{\ln 3} t \approx 4.99$

In 5 hours, the population will be 24,000.

Note

Remember to define all variables. The wording of the problem indicates both the initial and current amounts of bacteria present.

Q: If you used log instead of ln (or vice versa), will you reach the same final answer?

A: Yes, you can use either.