Suppose a colony of bacteria has a continuous growth rate of 18% per hour. By what percent will the colony have grown after 5 hours?
A) 40.7%
B) 246.0%
C) 60.7%
D) 146.0%

Question

Quizplus · Accepted Answer

The growth of the bacteria can be calculated using the formula for continuous growth: $A = P e^{rt}$, where $A$ is the amount after time $t$, $P$ is the initial amount, $e$ is the base of the natural logarithm (approximately 2.71828), $r$ is the rate of growth, and $t$ is the time in the same units as the rate. For an 18% growth rate per hour over 5 hours, the formula becomes $A = P e^{0.18 \times 5}$. Calculating this gives a growth factor of approximately 2.46, meaning the colony has grown 146% beyond its original size.

Suppose a Colony of Bacteria Has a Continuous Growth Rate