Question

In 1994, the moose population in a park was measured to be 3000. By 1998, the population was measuredagain to be 3400. If the population continues to change linearly:Find a formula for the moore population, P, in terms of t, the years since 1990.P(t)-What does your model predict the moose population to be in 2005?

Answer 1

We will consider a graph

Where x on the graph represent years since 1990 and y on the graph to represent the population of the moose

We have two points on the graph: ( 4, 3000) and (8, 3400)

Using the slope formula;

slope(m) = y₂-y₁ / x₂-x₁

=3400-3000 / 8-4

=400/4

=100

We can now use the slope formula to find the equation for the line;

y- y₁ = m (x- x₁)

y - 3000 = 100( x- 4)

y - 3000= 100x - 400

add 3000 to both-side of the equation

y-3000+3000=100x-400+3000

y= 100x + 2600

But the formula is in term of p and t

Hence, we will replace y by p and then x with t

p(t) = 100t + 2600

Hence, the above is the formula for the Moore population since 1990

To predict the moose population in 2005, we determine the years from 1990 to 2005

years = 2005 - 1990 = 15

substituting into the equation;

p(t) = 100t + 2600

p(15) = 100(15) + 2600

= 1500 + 2600

= 4100

p(15) = 4100

The model predict the moose population to be 4100 in 2005