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so namely, the "common difference" d = -4, and the first term a₁ = 7.
a.
so that for
or
. The derivative being equal to 0 gives you some information about the long-term stability of the population
; namely, that the carrying capacity is 1000.
b. If , then
and
, so that
, which means the population would be increasing.
c. If , then
but
, so
and the population would be decreasing.