$\"\"$ number of locations of a popular coffee house chain is (in millions) over the years is shown in following table.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Year	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$

(a)

Average rate of growth:

Average rate of growth is defined as $\"\"$

Average rate of growth $\"\"$ .

(i)

From $\"\"$ to $\"\"$ :

Observe the table.

In the year $\"\"$ , the number of US phone subscribers are $\"\"$ .

Number of locations of growth is $\"\"$ .

Average rate of locations growth from $\"\"$ to $\"\"$ is $\"\"$ .

(ii)

From $\"\"$ to $\"\"$ :

Observe the table.

In the year $\"\"$ , the number of US phone subscribers are $\"\"$ .

Average rate of locations growth from $\"\"$ to $\"\"$ is $\"\"$ .

(iii)

From $\"\"$ to $\"\"$ :

Observe the table.

In the year $\"\"$ , the number of US phone subscribers are $\"\"$ .

Average rate of locations growth from $\"\"$ to $\"\"$ is $\"\"$ .

(b)

Instantaneous rate of growth in $\"\"$ :

Consider two average rates of change of (ii) and (iii) that is $\"\"$ and $\"\"$ .

Instantaneous rate of growth in $\"\"$ is determined by taking average of $\"\"$ and $\"\"$ .

Instantaneous rate of growth in $\"\"$ : $\"\"$ .

(c)

Instantaneous growth in $\"\"$ by measuring the slope of tangent:

$\"\"$

Slope of the tangent $\"\"$ .

Observe the graph, $\"\"$ .

Instantaneous rate of growth in $\"\"$ is $\"\"$ million per year.

(d)

Instantaneous rate of growth in $\"\"$ :

Average rate of locations growth from $\"\"$ to $\"\"$ is $\"\"$ .

Instantaneous rate of growth in $\"\"$ is determined by taking average of $\"\"$ and $\"\"$ .

Instantaneous rate of growth in $\"\"$ $\"\"$ .

Instantaneous rate of growth in $\"\"$ is same as average rate of locations growth from $\"\"$ to $\"\"$ .

(a)

(i) Average rate of locations growth from $\"\"$ to $\"\"$ is $\"\"$ locations/year.

(ii) Average rate of locations growth from $\"\"$ to $\"\"$ is $\"\"$ locations/year.

(iii) Average rate of locations growth from $\"\"$ to $\"\"$ is $\"\"$ locations/year.

(b) Instantaneous rate of growth in $\"\"$ is $\"\"$ locations/year.

(d) Instantaneous rate of growth in $\"\"$ is $\"\"$ locations/year..