Question

Suppose a population of 250 crickets doubles in size every 3 months. How many crickets will there be after 2 years?

Answer 1

For geometric mean, the formula is An=A1r^(n)

n is the number of 3 months in two years: 3*8= 24; 24/3= 8 (3-month periods)

A1 is the initial population. r is the ratio which is 2 (doubles)

An=250*2^(8)= 64000 crickets

Answer 2

The equation that may be derived by the given conditions,
at = a1 x 2^(t / 3)
where at is the population of crickets at any time t in months, a1 is the initial population (250). Substituting the values to the equation,
at = (250) x 2^(2x12 / 3) = 64000

Thus, the population of crickets after 2 years is 64,000.