Mrs Garcia planted a pepper plant in a tomato plant in her garden The pepper plant is 6 in tall and gross 2 in each week The tomato plant is 4 in tall and gross 2 in each week which of the following statements is true about the heights of the two plants select all the answers that are true A The pepper plant is always taller than the tomato plant B after 2 weeks the tomato plant is taller than the pepper plant C after 3 weeks the tomato plant is taller than the pepper plant D after 4 weeks The tomato plants and the pepper plants are the same height E The tomato plant is always 2 in shorter than the pepper plant

Answer 1

Let's analyze the heights of the two plants over time based on their initial heights and weekly growth:

• Pepper Plant:

  • Initial height: 6 inches
  • Growth per week: 2 inches
  • Height after \( n \) weeks: \( 6 + 2n \)

• Tomato Plant:

  • Initial height: 4 inches
  • Growth per week: 2 inches
  • Height after \( n \) weeks: \( 4 + 2n \)

Now, let's evaluate the statements based on calculations:

1. At Week 0 (Initial Heights):

   • Pepper Plant: 6 inches
   • Tomato Plant: 4 inches
   • The pepper plant is taller.

2. After 1 Week:

   • Pepper Plant: \( 6 + 2(1) = 8 \) inches
   • Tomato Plant: \( 4 + 2(1) = 6 \) inches
   • The pepper plant is still taller.

3. After 2 Weeks:

   • Pepper Plant: \( 6 + 2(2) = 10 \) inches
   • Tomato Plant: \( 4 + 2(2) = 8 \) inches
   • The pepper plant is still taller.

4. After 3 Weeks:

   • Pepper Plant: \( 6 + 2(3) = 12 \) inches
   • Tomato Plant: \( 4 + 2(3) = 10 \) inches
   • The pepper plant is still taller.

5. After 4 Weeks:

   • Pepper Plant: \( 6 + 2(4) = 14 \) inches
   • Tomato Plant: \( 4 + 2(4) = 12 \) inches
   • The pepper plant is still taller.

6. After 5 Weeks:

   • Pepper Plant: \( 6 + 2(5) = 16 \) inches
   • Tomato Plant: \( 4 + 2(5) = 14 \) inches
   • The pepper plant is still taller.

7. After 6 Weeks:

   • Pepper Plant: \( 6 + 2(6) = 18 \) inches
   • Tomato Plant: \( 4 + 2(6) = 16 \) inches
   • The pepper plant is still taller.

8. Continuing in this way, we see that the pepper plant will always remain taller than the tomato plant as both are growing at the same rate, but the pepper plant started taller.

Now, let's evaluate the statements:

A. The pepper plant is always taller than the tomato plant.

• True.

B. After 2 weeks the tomato plant is taller than the pepper plant.

• False. The pepper plant is taller.

C. After 3 weeks the tomato plant is taller than the pepper plant.

• False. The pepper plant is taller.

D. After 4 weeks the tomato plant and the pepper plant are the same height.

• False. The pepper plant is taller.

E. The tomato plant is always 2 inches shorter than the pepper plant.

• True. The difference in height remains constant at 2 inches.

Answers: A and E are true statements.