Context: A sample of $530$ Bacillus megaterium cells doubles every $25$ minutes, and the task is the function $f$ giving the number of cells $x$ minutes after growth begins.

Answer: C) $f(x) = 530 \cdot 2^{x/25}$

Why? The starting count $530$ is the coefficient, and doubling means the growth factor is $2$. One doubling occurs per $25$ minutes, so $x$ minutes contain $\dfrac{x}{25}$ doublings, giving $f(x) = 530 \cdot 2^{x/25}$.

Traps:

• A) Base $\dfrac{1}{3}$ shrinks the sample to a third of its size every $25$ minutes, describing decay rather than growth.
• B) Base $\dfrac{1}{2}$ halves the population every $25$ minutes, the reverse of doubling.
• D) Base $3$ triples the count every $25$ minutes, a faster rate than the doubling the passage states.