A Review On A Hydroelectric Project Biology

If a hydroelectric project is expected to cerate a large lake into which some fish are to be placed, a biologist estimates that if 10,000 fish were introduced into the lake, the population of fish would increase by 50% in the first year, but the long-term sustainable limit would be about 60,000.

In order to estimate the growth rate of the population of fish, it is best to find a linear growth factor for. We do this by finding two ordered pairs in the form (u0, r0), (un, rn).

rn is the growth rate when the population is n.

since we know from the information given that when there are 60000 fish in the lake, the growth rate is stable i.e. 1, this can be represented as one of our ordered pairs: (60000, 1). We also know that when 10000 fish are in the lake, the growth rate is 50% i.e. population is multiplied by 1.5, so the second ordered pair is (10000, 1.5).

from these pairs we have:

r10000 = 1.5

r60000 = 1

and since we are trying to search for a linear function of the growth rate, we can also denote rn as:

rn = mn + b

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