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 varying from 0 to 10 months and show how the height, , increases every month. (iii) Find an expression that relates and , and explain why it represents linear growth.

We will find the plant's height using its initial height and monthly growth. Step 1 — Calculate height after 7 months Let's find how much the plant grows in 7 months. The plant grows by 0.5 feet each month. Now, we add this growth to the initial height. The initial height is 1.75 feet. > Step 2 — Create a table of values Let's make a table showing height for months from 0 to 10. The height starts at 1.75 feet. It increases by 0.5 feet every month. | t (months) | h (feet) | | :--------: | :------: | | 0 | 1.75 | | 1 | 2.25 | | 2 | 2.75 | | 3 | 3.25 | | 4 | 3.75 | | 5 | 4.25 | | 6 | 4.75 | | 7 | 5.25 | | 8 | 5.75 | | 9 | 6.25 | | 10 | 6.75 | Step 3 — Find the expression and explain linear growth Let be the height of the plant. Let be the number of months. The initial height is 1.75 feet. The plant grows by 0.5 feet per month. So, the height after months is: This expression shows linear growth. The height increases by a constant amount (0.5 feet) every month. This constant rate of change is a key feature of linear relationships. Answer > (i) The height after 7 months is 5.25 feet. > (ii) The table of values is: > | t (months) | h (feet) | > | :--------: | :------: | > | 0 | 1.75 | > | 1 | 2.25 | > | 2 | 2.75 | > | 3 | 3.25 | > | 4 | 3.75 | > | 5 | 4.25 | > | 6 | 4.75 | > | 7 | 5.25 | > | 8 | 5.75 | > | 9 | 6.25 | > | 10 | 6.75 | > (iii) The expression is . It represents linear growth because the height increases by a constant amount of 0.5 feet each month.

Introduction to Linear Polynomials | Exercise 2.4

Question 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.

Solution

We will find the plant's height using its initial height and monthly growth.

Step 1 — Calculate height after 7 months

Let's find how much the plant grows in 7 months. The plant grows by 0.5 feet each month.

$\text{Growth in 7 months} = 0.5 \times 7$

$= 3.5 \text{ feet}$

Now, we add this growth to the initial height. The initial height is 1.75 feet.

$\text{Height after 7 months} = 1.75 + 3.5$

$\boxed{5.25 \text{ feet}}$

Step 2 — Create a table of values

Let's make a table showing height $h$ for months $t$ from 0 to 10. The height starts at 1.75 feet. It increases by 0.5 feet every month.

| t (months) | h (feet) | | :--------: | :------: | | 0 | 1.75 | | 1 | 2.25 | | 2 | 2.75 | | 3 | 3.25 | | 4 | 3.75 | | 5 | 4.25 | | 6 | 4.75 | | 7 | 5.25 | | 8 | 5.75 | | 9 | 6.25 | | 10 | 6.75 |

Step 3 — Find the expression and explain linear growth

Let $h$ be the height of the plant. Let $t$ be the number of months. The initial height is 1.75 feet. The plant grows by 0.5 feet per month.

So, the height $h$ after $t$ months is:

$h = 1.75 + 0.5t$

This expression shows linear growth. The height increases by a constant amount (0.5 feet) every month. This constant rate of change is a key feature of linear relationships.

Answer

(i) The height after 7 months is 5.25 feet. (ii) The table of values is: | t (months) | h (feet) | | :--------: | :------: | | 0 | 1.75 | | 1 | 2.25 | | 2 | 2.75 | | 3 | 3.25 | | 4 | 3.75 | | 5 | 4.25 | | 6 | 4.75 | | 7 | 5.25 | | 8 | 5.75 | | 9 | 6.25 | | 10 | 6.75 | (iii) The expression is $h = 1.75 + 0.5t$ . It represents linear growth because the height increases by a constant amount of 0.5 feet each month.

Question 1

Answer

More questions in Exercise 2.4