algebra question (please help all parts)

Question

In 1993, the moose population in a park was measured to be 4230. By 1997, the population was measured again to be 4630. If the population continues to change linearly:

Find a formula for the moose population, P, in terms of t, the years since 1990.

P(t)=____________

What does your model predict the moose population to be in 2009?___________

Answer 1

In the 4 yrs between 1993 and 1997 the moose pop'n increased by 4630 - 4230, or 400. The linear slope is 400/4, or an increase of 100/yr. (m in the y = mx + b slope-intercept form). If 1993 is year 0 in the study, then b = 4230 when t = 0 in 1993.

y = 100x + 4230 or, to use the required variables, P = 100t + 4230.

2009 would be year 16 (2009 - 1993), then t = 16. Plug in and solve. Hope there's room for them all!

Answer 2

Assuming a linear model,

P(t) = mt + b

Where m is the slope and b is the initial population in 1990.

slope = (change in population)/(change in time) = (4630-4230)/(1997-1993) = 400/4 = 100

Three years earlier, the population would have been 3×100 less or 4230 - 300 = 3930

P(t) = 100t + 3930

In 2009, t = 2009-1990 = 19

P(19) = 100(19) + 3930 = 1900 + 3930 = 5830