Question

In 1994, the moose population in a park was measured to be 3080. By 1997, the population was measured again to be 3320. Of the population continues to change linearly: Find a formula for the moose population, P , in terms of t , the years since 1990

Answer 1

Answer:

the formula for the moose population is P(t) = 80t + 2760

Step-by-step explanation:

To get the the formula of the population which changes linearly we start by;

let x be the number of years since year 1990 and y be the number of population measured.

in year  1994 x = 4, y = 3080

            1997 x = 7, y = 3320

we have just gotten two points on a graph which are (4, 3080) and (7, 3320).

Using the slope formula  m = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

by substituting both points into the equation

m = (3080 - 3320) / (4 - 7)

m = (-240) / (-3)

m =  80

After getting the slope, we will use the point slope formula to get the equation of the line.  (NOTE: Also either points will arrive at the same result)

point-slope formula = $y- y_1 = m(x - x_1)$

by substituting the first point into the equation and the slope,

             y - 3080 = 80 (x - 4)

             y - 3080 = 80x - 320

by adding 3080 to both sides

             y - 3080 + 3080 = 80x -320 + 3080

            y = 80x + 2760

so by replacing the formula in terms of P and t, we replace y with P(t) and x with t

          P(t) = 80t + 2760

also by using the second point into the equation and the slope,

             y - 3320 = 80 (x - 7)

             y - 3320 = 80x - 560

by adding 3320 to both sides

           y - 3320 + 3320 = 80x - 560 + 3320

            y = 80x + 2760