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

Question

In 1992, the moose population in a park was measured to be 4760. By 1999, the population was measured again to be 3990. If the population continues to change linearly:

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

B.) What does your model predict the moose population to be in 2008?

Answer 1

A linear equation has the form y = mx + b (the slope intercept form) where m = gradient and b = y intercept.

In this case, we have P = mt + b where P = population and t = years since 1990.

We have two values of P and t, so we will get simultaneous equations in m and b to solve.

1992 for (2, 4760) we have 4760 = m(2) + b = 2m + b

1999 for (9, 3990) we have 3990 = m(9) + b = 9m + b

we can immediately subtract to eliminate b,

2m + b = 4760

-

9m + b = 3990

=

-7m + 0b = 770

=> m = -110

then substitute m to find b in 2(-110) + b = 4760

=> b = 4760 + 220 = 4980

(A) hence our required equation is P = 4980 - 110t

(B) In 2008, t = 18, hence P = 4980 - 110(18) = 3000 moose

In addition, it's quite easy to find the intercepts when t = 0 and P = 0. At year 0 (1990) the initial population is the y intercept, 4,980 moose. And no moose are left when P = 0 or 4980/110 = 45.27 years, or early in 2035.

For these types of questions I highly recommend Desmos graphing calculator.