Calculus Moose Question

Question

In 1994, the moose population in a park was measured to be 3660. By 1997, the population was measured again to be 4320. If the population continues to change linearly: Find a formula for the moose population, P , in terms of t, the years since 1990. What does your model predict the moose population to be in 2008?

Answer 1

In 1994 we have t = 4 and P = 3660. In 1997 t = 7 and P = 4320

P(t) = mt + b; m = (4320 - 3660)/(7 - 4) = 220; P(t) = 3660 + 220(t - 4); P(t) = 220t + 2780

In 2008 t = 18 and P(18) = 220·18 + 2780 = 6740

Answer 2

Let t be the number of years since 1994 and P be the moose population.

Since this is linear, the formula for the population is:

P(t) = mt + P₀

Where P₀ is the initial population of 3660. Three years later, the population is 4320, so the slope, m is:

m = ΔP/Δt = (4320-3660)/3 =220

P(t) = 220t + 3660

14 years after 1994, in 2008, the population will be

P(14) = 220(14)+3660 = 6740