Q1. Page 25: 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.
Answer:
(i) Height after 7 months:
Height = 1.75 + 0.5(7) = 1.75 + 3.5 = 5.25 feet
(ii) Table of values:
| Month (t) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Height (h) in feet | 1.75 | 2.25 | 2.75 | 3.25 | 3.75 | 4.25 | 4.75 | 5.25 | 5.75 | 6.25 | 6.75 |
(iii) Linear Expression:
h(t) = 1.75 + 0.5t
This represents linear growth because the height increases by a constant amount (0.5 feet) each month.
Q2. Page 25: 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.
Answer:
(i) Value after 3 years:
Value = 10000 - 800(3) = 10000 - 2400 = ₹7600
(ii) Table of values:
| Year (t) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| Value (v) in ₹ | 10000 | 9200 | 8400 | 7600 | 6800 | 6000 | 5200 | 4400 | 3600 |
(iii) Linear Expression:
v(t) = 10000 - 800t
This represents linear decay because the value decreases by a constant amount (₹800) each year.
Q3. Page 25: 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.
Answer:
Population after 6 years:
Population = 750 + 50(6) = 750 + 300 = 1050
The population after 6 years will be 1050.