The resident population of South Carolina was 3860 in 1997 and 4107in 2002. Assume that the relationship between the population y andthe year t is linear. Let t=7 represent 1997. a)Write a linear model for the data. What is the slope and what does it tell you about the population. b)Estimate the population in 1999.

depistetzwy

depistetzwy

Open question

2022-09-02

The resident population of South Carolina was 3860 in 1997 and 4107in 2002. Assume that the relationship between the population y andthe year t is linear. Let t=7 represent 1997.
a)Write a linear model for the data. What is the slope and what does it tell you about the population.
b)Estimate the population in 1999.

Answer & Explanation

Allyson Vance

Allyson Vance

Beginner2022-09-03Added 14 answers

Since the graph is linear y=mx+b, and you are given the two points (7,3860) and (12,4107), to find the slope y 2 y 1 / t 2 t 1
(4107-3860)/(12-7)=247/5=49.4
y=49.4t+b (plug in one of the points to get b)
3860=49.4*7+b 3860=345.8+b b=3514.2
Making your final equation y=49.4t+3514.2
To find the population in 1999 (t=9) simply plug ntoequation
y=(49.4*9)+3514.2
y=3958.8
Tamara Anthony

Tamara Anthony

Beginner2022-09-04Added 2 answers

First you find the rate of change
t= number of years after 1990
P= population
P=3860 when t= 7
and
P=4107 when t=12
so (4107-3860)(12-7)
slope is 49.4
This tells us that the population will increase approximately 49.4 for every increase of year by 1
P=49.4t + +3514.2
P(1999) = 3958.8

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?