Question

The bacteria population in a petri dish was 14 at the beginning of an experiment. After 30 minutes the population of 20 in after an hour the population of 56

Answer 1

The answer is below

Explanation:

A geometric sequence is a sequence such that each term after the first is found by multiplying the previous one by a fixed number (common ratio). It is given by:

`a_n=ar^(n-1)\\\\n=1,2,3,\ .\ .\ .`

where a is the first term, r is the common ratio.

From the question, the first term is 14 (at n = 1). a₁ = 14

After 30 minutes (n = 2), the population is 28. a₂ = 28

After 1 hour (n = 3), the population is 56. a₃ = 56

Common ratio (r) = a₃/a₂ = a₂/a₁ = 56 / 28 = 28/14 = 2

a) This sequence is represented as:

`a_n=14(2)^(n-1)`

b) After 4 hours, that is n = 9:

`a_9=14(2)^(9-1)=14(2)^8=3584`