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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. (1 point) The plants will be exactly the same height during week . Skip to navigation

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To represent the growth of the two plants, we can set up the following equations:

For Plant A:

  • Initial height = 8 inches
  • Growth rate = 3 inches per week

The equation for Plant A, where \(x\) is the number of weeks and \(y\) is the height in inches, is: \[ y = 8 + 3x \]

For Plant B:

  • Initial height = 12 inches
  • Growth rate = 2 inches per week

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

Question 2: When will the plants be exactly the same height?

To find out when the plants will be the same height, we need to set the two equations equal to each other:

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

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

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

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

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

Thus, the answers to the questions are:

  • Plant A: \(y = 8 + 3x\)
  • Plant B: \(y = 12 + 2x\)
  • The plants will be exactly the same height during week 4.