In 1992, the moose population in a park was measured to be 3590. By 1999, the population was measured again to be 4500. If the population continues to change linearly
A.) Find a formula for the moose population, P, in terms of t, the years since 1990.
P(t)= ____

B.) What does your model predict the moose population to be in 2006?

Given the ordered pairs (t, P(t)) = (2, 3590) and (9, 4500), you want a linear model that describes the relation. You also want the value of P(16).

A.) Linear model

We can write the formula for P(t) starting with the point-slope equation for P in terms of t. To do that, we need the slope:

m = (P2 -P1)/(t2 -t1)

m = (4500 -3590)/(9 -2) = 910/7 = 130

The point-slope equation will be ...

P -P1 = m(t -t1)

P -3590 = 130(t -2)

Solving for P, we find ...

P = 130t -260 +3590 . . . . . eliminate parentheses, add 3590

P(t) = 130t +3330

B.) Prediction

The value of P(16) will be ...

P(16) = 130(16) +3330 = 2080 +3330 = 5410

The moose population is predicted to be 5410 in 2006.

__

Additional comment

The value of t is years since 1990, so the relevant values are ...

1992: t = 1992 -1990 = 2

1999: t = 1999 -1990 = 9

2006: t = 2006 -1990 = 16

tutorconsortium201 tutorconsortium201 · Answer 2 · 2022-09-27T05:42:59-04:00

Values of moose population by linear model A.) P(t) = 130t +3330 B.) P(16) = 5410

What does the term "linear model" mean?

In a linear model, the terms are added rather than multiplied, divided, or provided as a non-algebraic function, as has been the case thus far in this section.
A linear model is not just a straight line or its higher dimensional equivalent.

Given the ordered pairs (t, P(t)) = (2, 3590) and (9, 4500), you want a linear model that describes the relation. You also want the value of P(16).

A.) Linear model

We can write the formula for P(t) starting with the point-slope equation for P in terms of t. To do that, we need the slope:

m = (P2 -P1)/(t2 -t1)

m = (4500 -3590)/(9 -2) = 910/7 = 130

The point-slope equation will be

P -P1 = m(t -t1)

P -3590 = 130(t -2)

Solving for P, we find

P = 130t -260 +3590 . . . . . eliminate parentheses, add 3590

P(t) = 130t +3330

B.) Prediction

The value of P(16) will be

P(16) = 130(16) +3330 = 2080 +3330 = 5410

The moose population is predicted to be 5410 in 2006.

(B) The value of t is years since 1990, so the relevant values are

1992: t = 1992 -1990 = 2

1999: t = 1999 -1990 = 9

2006: t = 2006 -1990 = 16

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