Question

John and Raul each bought a plant on the same day. John's plant was initially taller than Raul's plant. Raul's plant grows at a faster rate than John's plant. Which pair of equations could model the height, h, of the plants after w weeks from the purchase?
A.John's plant: h=w2+3 Raul's plant: h=w+1
b.John's plant: h=3w+4 Raul's plant: h=w+6
c. John's plant: h=w2+2Raul's plant: h=2w+5
D. John's plant: h=w2+5 Raul's plant: h=w2+3

Answer 1

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➷ We would want the equation for Raul's plant to give a larger value. Try the value 2 for weeks to find the pair of equations that give Raul's plant a larger value.

After trying this, you'll find that the answer is C.

Here is how I tried it with the value of 2 weeks:

John's plant: h = (2)^2 + 2 = 6

Raul's plant: h = 2(2) + 5 = 9

As you can see, Raul's plant would have a larger height with this pair of equations so it must be correct.

In short, the answer is option C.

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Answer 2

Answer:

Step-by-step explanation:

Let the plant's height be h after w weeks from the purchase.

John's plant was initially taller than Raul's plant. So h for John's plant > h for Raul's plant when w=0.

For A, when w=0, John's plant: h=3 and Raul's plant: h=1  so it satisfies the above.

For B, when w=0, John's plant: h=4 and Raul's plant: h=6 so it is not the answer.

For C, when w=0, John's plant: h=2 and Raul's plant: h=5 so it is not the answer.

For D, when w=0, John's plant: h=5 and Raul's plant: h=3 so it satisfies the above.

Raul's plant grows at a faster rate than John's plant.

For A, John's plant: h grows at w2 and Raul's plant: h grows at w so it is not the answer.

The only answer left is D.