Question

rowie is tracking the progress of her plants growth. today the plant is 5cm high. The plant grows 2cm per day.

Write a liner model that represents tha height of the plants after x days.

Graph the number of days against the growth of the plants. ​

Answer 1

Given:

Rowie is tracking the progress of her plant's growth. today the plant is 5cm high

The plant grows 2cm per day

To find:

(1). Write a liner model that represents the height of the plants after x days.  

(2). Graph the number of days against the growth of the plants.

Solution:

(1). Finding the linear model:

Let's assume,

"h" → the height of the plant after x days

"x" → the no. of days

The present height of the plant = 5 cm

The rate of growth of the plant = 2 cm/per day

Now, we can write the linear model that represents the height of the plants after x days as follows:

$\boxed{\bold{h = 2x + 5}}$

(2). Plotting the graph:

Referring to the graph attached below, we can assume

The no. of days → "x" → represented by the x-axis

The growth or height of the plants → "h" → represented by the y-axis

Since the present-day height of the is given, so considering the present-day as x = 0

Linear equation:⇒ h = 2x + 5

Now, let's put the values for h and x:

(i). x = 0

Then, h = (2 × 0) + 5 = 5

(ii). x = 2.5

Then, h = (2 × 2.5) + 5 = 5 + 5 = 10

(iii). x = 5

Then, h = (2 × 5) + 5 = 10 + 5 = 15

Thus, plotting the graph with the following points:

x-axis ⇒ x ⇒ 0 | 2.5 | 5

y-axis ⇒ h ⇒ 5 | 10  | 15

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Answer 2

Step-by-step explanation:

In order to find a linear model for the given situation, we first consider the general mathematical framework which is

y = mx + c

Here m is the gradient or slope of line, c is the y intercept.

Now considering given situation

let the length of tree across y axis and number of days across x axis

To find the slope;

m = (15-5)/5

m = 2

C intercept = 5

Hence the linear model would be

Lenght of tree = 2 × Number of days + 5