Answer:
The answer is below
Step-by-step 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:
[tex]a_n=ar^{n-1}\\\\n=1,2,3,\ .\ .\ .[/tex]
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:
[tex]a_n=14(2)^{n-1}[/tex]
b) After 4 hours, that is n = 9:
[tex]a_9=14(2)^{9-1}=14(2)^8=3584[/tex]
