Answer :
Certainly! Let's tackle each part of the question step by step.
### Part a: Represent the ratio relationship using a graph.
To plot the growth over time, we need to understand that the growth rate is consistent, meaning it's a linear relationship. For every 2 months, you grow 3 centimeters.
1. Identify the ratio:
- Growth per month = [tex]\( \frac{3 \text{ cm}}{2 \text{ months}} = 1.5 \text{ cm/month} \)[/tex]
2. Set up the data points:
- To visualize this, we can consider a range of months and calculate the corresponding growth:
- 0 months: 0 cm (initial point)
- 1 month: [tex]\( 1.5 \text{ cm} \times 1 \text{ month} = 1.5 \text{ cm} \)[/tex]
- 2 months: [tex]\( 1.5 \text{ cm} \times 2 \text{ months} = 3 \text{ cm} \)[/tex]
- 3 months: [tex]\( 1.5 \text{ cm} \times 3 \text{ months} = 4.5 \text{ cm} \)[/tex]
- Continue this pattern up to 10 months.
3. Plot the graph:
- On the x-axis, represent the time in months.
- On the y-axis, represent the growth in centimeters.
- Ensure your graph shows a straight line indicating a consistent growth rate.
Here is a table of the data points we'll use:
[tex]\[ \begin{array}{c|c} \text{Months (x)} & \text{Growth in cm (y)} \\ \hline 0 & 0 \\ 1 & 1.5 \\ 2 & 3.0 \\ 3 & 4.5 \\ 4 & 6.0 \\ 5 & 7.5 \\ 6 & 9.0 \\ 7 & 10.5 \\ 8 & 12.0 \\ 9 & 13.5 \\ 10 & 15.0 \\ \end{array} \][/tex]
### Part b: Calculate growth in 5 months
We have established the growth rate as [tex]\(1.5 \text{ cm/month}\)[/tex].
To find out how much you grow in 5 months, we simply multiply the growth rate by the number of months:
[tex]\[ \text{Growth in 5 months} = 1.5 \text{ cm/month} \times 5 \text{ months} = 7.5 \text{ cm} \][/tex]
So, at this rate, you will grow 7.5 centimeters in 5 months.
### Summary:
- Graph Representation: A straight line graph with a slope of 1.5, starting from (0, 0) and increasing, where x is the number of months and y is the growth in centimeters.
- Growth Calculation: In 5 months, you will grow 7.5 centimeters.
### Part a: Represent the ratio relationship using a graph.
To plot the growth over time, we need to understand that the growth rate is consistent, meaning it's a linear relationship. For every 2 months, you grow 3 centimeters.
1. Identify the ratio:
- Growth per month = [tex]\( \frac{3 \text{ cm}}{2 \text{ months}} = 1.5 \text{ cm/month} \)[/tex]
2. Set up the data points:
- To visualize this, we can consider a range of months and calculate the corresponding growth:
- 0 months: 0 cm (initial point)
- 1 month: [tex]\( 1.5 \text{ cm} \times 1 \text{ month} = 1.5 \text{ cm} \)[/tex]
- 2 months: [tex]\( 1.5 \text{ cm} \times 2 \text{ months} = 3 \text{ cm} \)[/tex]
- 3 months: [tex]\( 1.5 \text{ cm} \times 3 \text{ months} = 4.5 \text{ cm} \)[/tex]
- Continue this pattern up to 10 months.
3. Plot the graph:
- On the x-axis, represent the time in months.
- On the y-axis, represent the growth in centimeters.
- Ensure your graph shows a straight line indicating a consistent growth rate.
Here is a table of the data points we'll use:
[tex]\[ \begin{array}{c|c} \text{Months (x)} & \text{Growth in cm (y)} \\ \hline 0 & 0 \\ 1 & 1.5 \\ 2 & 3.0 \\ 3 & 4.5 \\ 4 & 6.0 \\ 5 & 7.5 \\ 6 & 9.0 \\ 7 & 10.5 \\ 8 & 12.0 \\ 9 & 13.5 \\ 10 & 15.0 \\ \end{array} \][/tex]
### Part b: Calculate growth in 5 months
We have established the growth rate as [tex]\(1.5 \text{ cm/month}\)[/tex].
To find out how much you grow in 5 months, we simply multiply the growth rate by the number of months:
[tex]\[ \text{Growth in 5 months} = 1.5 \text{ cm/month} \times 5 \text{ months} = 7.5 \text{ cm} \][/tex]
So, at this rate, you will grow 7.5 centimeters in 5 months.
### Summary:
- Graph Representation: A straight line graph with a slope of 1.5, starting from (0, 0) and increasing, where x is the number of months and y is the growth in centimeters.
- Growth Calculation: In 5 months, you will grow 7.5 centimeters.
