Geometric sequences that represent phenomena or compartments of daily life

Answer 1

1) Compound interest: When calculating compound interest, the balance grows exponentially over time. The sequence representing the growth of the balance would be a geometric sequence.

2) Population growth: In certain animal populations, the growth rate follows geometric progression. For example, if a pair of rabbits can produce two offspring per year and each offspring pair can further reproduce, the population will grow exponentially over time.

3) Bacterial growth: Bacteria reproduce through binary fission, doubling their population with each generation. The growth of bacterial colonies can be modeled using a geometric sequence.

4) Radioactive decay: The decay of radioactive elements follows a geometric sequence. The number of radioactive atoms decreases exponentially over time as they decay into stable forms.

5) Musical notes: In a musical scale, the frequency ratios between adjacent notes often follow geometric progressions. For example, in the diatonic scale, the frequency ratio between adjacent notes is usually 2^(1/12).

6) Branching patterns in trees: The number of branches at each level of a tree follows a geometric sequence. For example, a tree may have 1 trunk, 2 primary branches, 4 secondary branches, 8 tertiary branches, and so on.

7) Digital image compression: When compressing images using techniques like block-based coding or wavelet compression, the levels of detail are often represented using geometric sequences. Each level of detail (such as different frequency bands) is encoded separately.

8) Population in a multi-level marketing system: In a multi-level marketing system, each person recruits a fixed number of new members, who then recruit more members, and so on. The size of the network at each level can be represented by a geometric sequence.

9) Spread of infectious diseases: In some cases, the rate of spread of an infectious disease can be modeled using a geometric sequence. Each infected person, on average, infects a fixed number of new people, resulting in exponential growth of the infected population.

10) Traffic congestion: The build-up of traffic congestion at a specific location can follow a geometric sequence. As more vehicles join the traffic, the congestion level may increase exponentially until it reaches a saturation point.