A new farm pond was stocked with 2500 crappies in 2003 The c

A new farm pond was stocked with 2500 crappies in 2003. The crappie population in 2006 was found to be 4320.

a)   Let t be the number of years after 2003 (in other words t = 0 corresponds to 2003). Write down the initial crappie population at t = 0.

Solution

The crappie population in the pond has increased from 2500 to 4320 in 3 years ( i.e. from 2003 to 2006). The increase in population, per, year, from 2003 is (4320 - 2500) / 3 = 1820/3. If p₀ be the initial population and p_t be the crappie population after t years, then p_t = p₀ + (1820/3)t so that p₀ = p_t -  (1820/3)t .

Note:

In the absence of other information, it has been assumed that the growth of crappies is linear.