Biologists estimate that the number of deer in Rhode Island in 2003 was 1,028, and in 2008 it had grown to 1,488. Biologists would like to model the deer population, p, as a function of the years, t, since 2000.

(a) Represent the information we have been told as two coordinate points. Be careful to know what your values of time are for each year.
(b) Calculate ∡p ÷ ∡t from 2003 to 2008. Include proper units in your answer.
(c) Give a physical interpretation of the value you found in part (b).
(d) Determine a linear relationship between the deer population, p, and the years since 2000, t.
(e) How many deer does this model predict were in Rhode Island in the year 2000? What does this represent about the linear function?
(f) How many deer does the model predict for Rhode Island now?

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joaobezerra joaobezerra · Answer 1 · 2022-11-11T13:15:42+01:00

a) The points are given as follows: (3, 1028) and (8, 1488).

b) The rate of change is:

c) The interpretation of the rate of change is that it gives the yearly increase in the number of deers.

d) The equation is: y = 92x + 752.

e) The prediction for the year of 2000 is the intercept of the function, which is of 752 deer.

f) The prediction for the current year of 2022 is of 2776 deer.

The slope-intercept representation of a linear function is:

y = mx + b

The coefficients of the function and their meaning in the context of this problem are listed as follows:

m is the slope of the function, representing the change in the output variable y when the input variable x increases by one. Hence, in this problem, it represents the yearly increase in the number of deer.

b is the y-intercept of the function, which is the value of the function when it's graph crosses the y-axis, that is, when x = 0. Hence, in this problem, it gives the population of deer in the year of 2000.

Considering the reference year 2000 as year 0, the coordinate points of the function are given as follows:

(3, 1028), (8, 1488).

Given two points, the slope of the function is given by the change in the output divided by the change in the input, hence:

m = (1488 - 1028)/(8 - 3) = 92.

Hence the function is:

y = 92x + b.

When x = 3, y = 1028, hence the intercept b is obtained as follows:

1028 = 92(3) + b

b = 1028 - 92(3)

b = 752.

Then:

y = 92x + 752.

2022 is 22 years after 2000, hence the estimate for the number of deer is given as follows:

y = 92(22) + 752 = 2776.

A similar problem, also featuring linear functions, is presented at https://brainly.com/question/24808124

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