EXERCISE 2.4
1. Suppose a plant has height 1.75 feet and it grows by 0.5 feet each
month.
(i) Find the height after 7 months.
(ii) Make a table of values for t varying from 0 to 10 months and
show how the height, h, increases every month.
(iii) Find an expression that relates h and t, and explain why it
represents linear growth.
2. A mobile phone is bought for `10,000. Its value decreases by
`800 every year.
(i) Find the value of the phone after 3 years.
(ii) Make a table of values for t varying from 0 to 8 years and
show how the value of the phone, v, depreciates with time.
(iii) Find an expression that relates v and t, and explain why it
represents linear decay.
3. The initial population of a village is 750. Every year, 50 people
move from a nearby city to the village.
(i) Find the population of the village after 6 years
(ii) Make a table of values for t varying from 0 to 10 years and
show how the population, P, increases every year.
(iii) Find an expression that relates P and t, and explain why it
represents linear growth.
4. A telecom company charges `600 for a certain recharge scheme.
This prepaid balance is reduced by `15 each day after the recharge.
(i) Write an equation that models the remaining balance b(x)
after using the scheme for x days. Explain why it represents
linear decay.
(ii) After how many days will the balance run out?
(iii) Make a table of values for x varying from 1 to 10 days and
show how the balance b(x), reduces with time.
2.5 Linear Relationships
A linear relationship represents the relationship between two
variables x and y, and can be expressed as y = ax + b.
Let us revisit the growing pattern of square tiles in Fig. 2.4. If x
represents the number of the term and y represents the numbers of
square tiles, then the linear relationship between x and y is expressed
as y = 2x – 1.
Sometimes, we may be required to find the linear relationship
between two quantities.
Example 11: A telecom company charges a fixed monthly fee and
an additional cost per GB of the internet data used. A student observes
that when she used 10 GB, her bill was `350. When she used 20 GB, her
bill was `550. If the monthly bill y depends on the amount of data used,
x (in GB), according to the relation y = ax + b, find the values of a and b.
Note that x = number of GB of the internet data used and y = total
monthly cost in Rupees.
To find the linear relationship y = ax + b, we note that when x = 10,
y = 350. Also, when x = 20, y = 550. We substitute these in y = ax + b to
arrive at the following equations.
350 = 10a + b and 550 = 20a + b
We solve these as follows: Let b = 350 – 10a (from the first equation).
We substitute this in the second equation to obtain
550 = 20a + (350 – 10a)
Thus, 550 = 10a + 350 or 10a = 200. So, a = 20. This leads to
b = 350 – 10a = 350 – 200 = 150.
We substitute the values of a and b in the equation y = ax + b to
obtain y = 20x + 150.
Thus, y = 20x + 150 represents the linear relationship between y,
the bill amount in Rupees, and x, the number of GB of the internet
data used.
Think and Reflect
Can you guess what the numbers 20 and 150 in the equation y = 20x + 150
represent?