Answer to Question #196457 in Linear Algebra for Tshepang

Question

The population of South Africa (in millions) was 52 million in 2011 and 56.2 million in 2016. 

Assume that the relationship between the 

y

and the year 

t

is linear. Let 

t = 0

represent 2011.

1.1.1 Write a linear model for the data. What is the slope and what it tells you 

about the population?

Answer 1

Let we assuming t om x axis-

As 2011 denote t=0 and 2016 denote t=5

Then The required points are-

(0,52) and (5,56.2)

Slope between these two points-

$m=\dfrac{56.2-52}{5-0}=\dfrac{4.2}{5}=0.84$

As The relationship between y and t is linear-

So Linear Model is-

$(y-52)=m(x-0)\\\Rightarrow y=0.84x+52$

Slope = 0.84

This means That the time increases fast as compared to the population.