Exercise 2.3
Solve the following:
1. A student has `500 in her savings bank account. She gets `150 every
month as pocket money. How much money will she have at the end
of every month from the second month onwards? Find a linear
expression to represent the amount she will have in the ninth month.
2. A rally starts with 120 members. Each hour, 9 members drop out of
the group. How many members will remain after 1, 2, 3, … hours?
Find a linear expression to represent the number of members at
the end of the nth hour.
3. Suppose the length of a rectangle is 13 cm. Find the area if the
breadth is (i) 12 cm, (ii) 10 cm, (iii) 8 cm. Find the linear pattern
representing the area of the rectangle.
4. Suppose the length of a rectangular box is 7 cm and breadth
is 11 cm. Find the volume if the height is (i) 5 cm, (ii) 9 cm,
(iii) 13 cm. Find the linear pattern representing the volume of the
rectangular box.
5. Sarita is reading a book of 500 pages. She reads 20 pages every
day. How many pages will be left after 15 days? Express this as a
linear pattern.
2.4. Linear growth and linear decay
Linear expressions help to model situations or phenomena where
there is growth or decline. Consider the following examples:
Example 9: The cost of a journey is given by the linear function
C(d) = 100 + 60d, where C indicates total cost in rupees and d the
distance travelled in km. Let us make a table of values for d varying
from 0 to 10 km and show how the cost increases for every km.
In this example, as the value of d increases by one km, the value
of the cost function C, increases by a fixed amount of `60. This is an
example of linear growth.
Think and Reflect
What is the cost for travelling 15 km? For how many kilometres will the cost
of the journey be `700?
Example 10: The height of water in a cylindrical tank is 3 m at the
start of summer. The height h m at the end of t months is given by the
linear function h(t) = 3 – 0.5t.
In the example above, as the value of t increases by a fixed number
(one month), the value of the height h decreases by a fixed number
(0.5). Therefore, this example represents linear decay.
Think and Reflect
What will be the height of the water at the end of 5 months?
Linear growth describes a linear pattern where a quantity increases by a
constant amount over equal intervals. Similarly, linear decay describes
a linear pattern where a quantity decreases by a constant amount over
equal intervals.