Answer
(a) $P=3000+200 t$.
(b) $P=3000(1.06)^t$.
(c) $P=3000 e^{0.06 t}$.
(d) $P=3000-50 t$.
(e) $P=3000(0.96)^t$.
(f) $P=3000 e^{-0.04 t}$.
Work Step by Step
(a) Since the population is growing by a constant rate, the function can be modelled as linear function,$b= 3000$ and $m= 200$ $$P=3000+200 t$$.
(b) Since the population is growing by a constant percent rate, the function can be modelled as an exponential function,$a= 3000$ and $b= 1.06$ $$P=3000(1.06)^t$$.
(c) Since the population is shrinking by a constant continuous percent rate, the function can be modelled as an exponential function,$a= 3000$ and $b= 0.06$ and $$P=3000 e^{0.06 t}$$.
(d) Since the population is shrinking by a constant rate, the function can be modelled as linear function,$b= 3000$ and $m= -50$
$$P=3000-50 t$$.
(e) Since the population is shrinking by a constant continuous percent rate, the function can be modelled as an exponential function,$a= 3000$ and $b=1- 0.04= 0.96$ and
$$P=3000(0.96)^t$$.
(f) Since the population is shrinking by a constant continuous percent rate, the function can be modelled as an exponential function,$a= 3000$ and $b= 0.04$
$$P=3000 e^{-0.04 t}$$.
