Question

A population of bacteria contains 120 bacteria in generation 1 and triples in

population every generation. This sequence represents the number of
bacteria for the first few generations:
120, 360, 1080, ...
What is the explicit formula for the number of bacteria in generation n?​

Answer 1

Bacteria population In generation n

pₙ = 120 (3ⁿ⁻¹)

Step-by-step explanation:

The pattern that the bacteria Population follws a geometric series' pattern with the first term equal to the population in the first generation, 120 bacteria, the population in the second generation is the second term and so on.

First term = a = population in the first generation = 120

Second term = a₂ = population in the second generation = 360

Third term = a₃ = population in the third generation = 1080

The general formula for any term of a geometric series is

aₙ = arⁿ⁻¹

a = first term

r = common ratio

But for a geometric series, common ratio is given as the next term divided by the very previous term.

r = (aₙ/aₙ₋₁)

For this question,

r = (360/120) = (1080/360) = 3

So, the right model for the profits for any given year n is

pₙ = 120 × 3ⁿ⁻¹

pₙ = 120 (3ⁿ⁻¹)

Hope this Helps!!!