Thread: geometric and arithmetic sequences

On an island the population of a species of insect (species A) is increasing geometrically, with a population of 25,000 in 1990 & an annual growth rate of 13.5%. Another species of insect (species B) is increasing in population arithmetically with numbers 37,000 in 1990 & an annual increment of 3500.

1. determine the difference in the numbers of the 2 species for each year during a decade (up to 1999)
2. In what year will species A be greater in number than species B? Assuming the growth rates remain fixed.

A scientist has a mathematical model where the species can cohabit provided that they have equal numbers in the year 2000.

3. If the growth rate in species A is to remain unchanged, what would the annual increment in species B need to be to achieve this?
4. If the annual increment in species B is to remain unchanged, what would the growth rate in species A need to be to achieve this?

1. You should know for an arithmetic sequence that



and for a geometric sequence that

.


So for species , the population during year is



and for species , the population during year is

.


2. You want species to be greater in number than species , so

.

You will need to use technology to solve this inequality for .