A research group observed that a certain bacterial culture triples in number every 5 years. In 2020, the number of bacteria in the culture was estimated to be 40. Based on this observation, which of the following equations correctly represents the population N(t) of bacteria after t years?
(a) N(t) = 40 × 3t
(b) N(t) = 40 × 3(t/5)
(c) N(t) = 40t × 3
(d) N(t) = 40 × (t/5)

Question

A research group observed that a certain bacterial culture triples in number every 5 years. In 2020, the number of bacteria in the culture was estimated to be 40. Based on this observation, which of the following equations correctly represents the population N(t) of bacteria after t years?
(a) N(t) = 40 &times; 3t
(b) N(t) = 40 &times; 3(t/5)
(c) N(t) = 40t &times; 3
(d) N(t) = 40 &times; (t/5)

ONLiNE UPSC · Accepted Answer

The bacterial culture triples every 5 years.
Initial population in 2020 = 40.
Let ttt be the number of years after 2020.
We're looking for an equation N(t) that shows population growth over time.
Every 5 years, the population triples:
&bull; At t = 0: N(0) = 40
&bull; At t = 5: N(5) = 40 &times; 3
&bull; At t = 10: N(10) = 40 &times; 32
&bull; At t =15: N(15) = 40 &times; 33, etc.
So, final equation: N(t) = 40 &times; 3(t/5)

Hence, option b is correct.

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A research group observed that a certain bacterial culture triples in number every 5 years. In 2020, the number of bacteria in the culture was estimated to be 40. Based on this observation, which of the following equations correctly represents the population N(t) of bacteria after t years? (a) N(t) = 40 × 3t (b) N(t) = 40 × 3(t/5) (c) N(t) = 40t × 3 (d) N(t) = 40 × (t/5)