Question

Kristin bought two sunflower plants. Plant A is 8 inches tall and is growing at a rate of 3 inches per week. Plant B is 12 inches tall and is growing at a rate of 2 inches per week. Write the two equations to represent each sunflower plant if the plants to continue to grow at the same rate. In your equations, x represents the number of weeks, and y represents the height of the plant in inches. (1 point) Plant A: y= Plant B: y= Question 2 When will the plants be exactly the same height?
This question requires you to show your work.
The plants will be exactly the same height during week

Answer 1

To represent the height of each sunflower plant as a function of time in weeks, we can create two equations based on the initial heights and growth rates provided.

**For Plant A:**
- Initial height: 8 inches
- Growth rate: 3 inches per week

The equation for Plant A is:
\[ y = 8 + 3x \]

**For Plant B:**
- Initial height: 12 inches
- Growth rate: 2 inches per week

The equation for Plant B is:
\[ y = 12 + 2x \]

Now we need to determine when the two plants will be exactly the same height. This means we need to set the equations for Plant A and Plant B equal to each other:

\[ 8 + 3x = 12 + 2x \]

Now, we can solve for \( x \):

1. Subtract \( 2x \) from both sides:
\[ 8 + 3x - 2x = 12 \]
\[ 8 + x = 12 \]

2. Subtract 8 from both sides:
\[ x = 12 - 8 \]
\[ x = 4 \]

So, the plants will be exactly the same height during **week 4**.