Chapter 8.9, Problem 7PPS

(a)

To determine

Graph of population v/s time .

Answer to Problem 7PPS

The rate of increasing population is higher in Illinois and they didn`t have same rate in any year

Explanation of Solution

Given data:

Table of population v/s time of Illinois and Pennsylvania

Formula used:

Slope intercept formula:-

  $y=mx+c$

Calculation:

Graph of population v/s time

  

We saw that the population of both cities are increasing at different rate.

Conclusion:

The rate of increasing population is higher in Illinois and they didn`t have same rate in any year

(b)

To determine

Point of intersection represent in the graph if it happen.

Answer to Problem 7PPS

It represent the both cities have same increasing rate.

Explanation of Solution

Given data:

Graph of population v/s time of Illinois and Pennsylvania

Formula used:

Slope intercept formula:-

  $y=mx+c$

Calculation:

Illinois was increased at faster because its graph had a faster increment. If two lines on graph intersect than it can be say that both cities have same increasing rate.

Conclusion:

It represent the both cities have same increasing rate.

(c)

To determine

Equation of the graph.

Answer to Problem 7PPS

Equation for Illinois is $25y=62x+312.5$

Equation for Pennsylvania is $50y=121x+605$

Explanation of Solution

Given data:

Graph of population v/s time of Illinois and Pennsylvania

Formula used:

Slope intercept formula:-

  $y=mx+c$

Calculation:

Equation for Illinois is

  $\begin{array}{l}y=\frac{12.4}{5}x+12.4\\ 25y=62x+312.5\\ \end{array}$(1)

Equation for Pennsylvania is

  $\begin{array}{l}y=\frac{12.1}{5}x+12.1\\ 50y=121x+605\end{array}$.........(2)

On intersection we have to find common points so by eq1 and eq2 we get

  $\frac{\frac{\begin{array}{l}(25y=62x+312.5)\times 2\\ 50y=121x+605\end{array}}{\begin{array}{l}\\ 50y=124x+625\\ 50y=121x+605\end{array}}}{\begin{array}{l}3x=-20\\ x=-6.6\\ y=-3.8\end{array}}$

So as we know year can`t be negative so there is no intersection point

Conclusion:

Equation for Illinois is $25y=62x+312.5$

Equation for Pennsylvania is $50y=121x+605$

(d)

To determine

Population of Illinois and Pennsylvania in 2015.

Answer to Problem 7PPS

Population in 2015 of Illinois is 4.9 billion and Pennsylvania is 4.8 billion.

Explanation of Solution

Given data:

Equation of population of Illinois and Pennsylvania

Formula used:

Slope intercept formula:-

  $y=mx+c$

Calculation:

Population in 2015 of

Illinois is 4.9 billion

And Pennsylvania is 4.8 billion.

Conclusion:

Population in 2015 of Illinois is 4.9 billion and Pennsylvania is 4.8 billion.