Question

Mathematics, 04.12.2019 23:31, datboyjulio21

For 1992 through 1994, the per capita consumption of fish and shellfish in the

u. s. increased at a rate that was approximately linear. in 1992, the per capita

consumption was 14.7 pounds, and in 1994 it was 15.1 pounds."

36. write a linear model for the per capita consumption of fish and shellfish

in the u. s. let t represent the number of years since 1992.

37. what would you expect the per capita consumption of fish and shellfish

to be in 2002?

Answer 1

• The linear model for the per capita consumption of fish and shellfish in the U.S. since 1992 is Consumption(t) = 14.7 + 0.2t.
• Using this model, the expected per capita consumption in 2002 would be 16.7 pounds.

Step-by-step explanation:

To create a linear model for the per capita consumption of fish and shellfish in the U.S., we observe that the consumption increased from 14.7 pounds in 1992 to 15.1 pounds in 1994.

This is an increase of 0.4 pounds over 2 years, or 0.2 pounds per year. Let t represent the number of years since 1992. The linear model would then be:

Consumption(t) = 14.7 + 0.2t

Using this model, to predict the per capita consumption in 2002, we plug in t = 10 (since 2002 is 10 years after 1992), leading to:

Consumption(10) = 14.7 + 0.2(10) = 14.7 + 2 = 16.7 pounds

Therefore, we would expect the per capita consumption of fish and shellfish to be 16.7 pounds in 2002.

Answer 2

The answer is below

Step-by-step explanation:

A linear equation is represented by the equation y = mx + b, where m is the rate of change, b is the value of y at x = 0, y is a dependent variable and x is an independent variable.

Let t represent the number of years since 1992, and P represent the per capita consumption of fish and shellfish in the U.S.

In 1992 (t = 0), the per capita consumption was 14.7 pounds, this can be represented by (0, 14.7) while in 1994 (t = 1994-1992=2) it was 15.1 pounds this can be represented by (2, 15.1)

Using (0, 14.7) and (2, 15.1) we can get the equation of the line using:

`P-P_1=(P_2-P_1)/(t_2-t_1)(t-t_1)\\ \\P-14.7=(15.1-14-7)/(2-0)(t-0)\\ \\P-14.7=0.2t\\\\P=0.2t+14.7`

In the year 2002 (t = 2002-1992 = 10), the per capita consumption of fish and shellfish is:

P = 0.2(10) + 14.7

P = 16.7 pounds