Question

Priya bought two plants for a science experiment. When she brought them home, the first plant was 5cm tall and the second plant was 4cm. Since then, the first plant has grown 0.5 cm a week and the second plant has grown 0.75 cm a week.

a. Which plant is taller at the end of 2 weeks? Explain your reasoning.

b. Which plant is taller at the end of 10 weeks? Explain your reasoning.

c. Priya represents this situation with the equation 5 + 0.5w = 4 + 0.75w, where w represents the end of week w. What does the solution to this equation, w = 4 represent in this situation?

d. what does the solution to the inequality 5 + 0.5w > 4 + 0.75w represent in this situation?​

Answer 1

a. After 2 weeks the first plant will be taller.

b. After 10 weeks the second plant will be taller.

c. After 4 weeks both the plant will be of the same height.

d. This is the condition for the height of the first plant is greater than that of the second plant.

Step-by-step explanation:

The first plant was 5 cm tall and the second plant was 4 cm.

Again, the first plant has grown 0.5 cm a week and the second plant has grown 0.75 cm a week.

So, the height of the first plant after W weeks will be (5 + 0.5W) cm. and the height of the second plant after W weeks will be (4 + 0.75W) cm.

a. After 2 weeks the first plant will be (5 + 2× 0.5) = 6 cm.

And after 2 weeks the second plant will be (4 + 2 × 0.75) = 5.5 cm

So, after 2 weeks the first plant will be taller.

b. After 10 weeks the first plant will be (5 + 10× 0.5) = 10 cm.

And after 10 weeks the second plant will be (4 + 10 × 0.75) = 11.5 cm

So, after 10 weeks the second plant will be taller.

c. If 5 + 0.5w = 4 + 0.75w, give w = 4 weeks, then this means that after 4 weeks both the plant will be of the same height.

d. If, 5 + 0.5w > 4 + 0.75w, then it means that this condition is for the height of the first plant will be more than the second plant. (Answer)