Question

a bean plant grow at a constant rate for a month. After 10, days, the plant is 25 centimeters tall. After 20 days, the plant is 45 centimeter tall
which equation models the height of the plant, y, after x days ?
A.y-25=1/2(x-10)
B.y+25=2(x+10)
C.y-25=2(x-10)
D.y-10=1/2(x-25)

Answer 1

C. y-25=2(x-10)

Step-by-step explanation:

If the growth of the plant is denoted by y cm and the number of days to spend to get that growth is x days, then we have two ordered pairs related to the growth of the plant and they are (10,25) and (20,45).

Now, the equation of the straight line on the coordinate plane that model the growth of the plant will be given by

$\frac{y - 45}{45 - 25} = \frac{x - 20}{20 - 10}$

⇒ y - 45 = 2(x - 20)

⇒ y - 25 = 2(x - 10)

So, this is the required equation that models the height of the plant, y , after x days. (Answer)

Answer 2

Given:

A bean plant grows at a constant rate for a month. After the first 10 days, the height of the plant is 25cm, after a total of 20 days the height of the plant is 45 centimeters.

To Find:

The equation model of the height of the plant(y) after x days.

Solution:

The given problem can be solved using the trial and error method.

1. After 10 days, the plant is 25cm tall. Hence, the value of x and y respectively in this case is 10, 25 respectively.

2. After 20 days, the plant is 45cm tall. Hence, the value of x and y respectively in this case is 20, 45 respectively.

Option A:

Case 1:

=> y - 25 = (x-10)/2, substitute the values x = 10 and y = 25,

=> 25 - 25 = (10 - 10)/2, 0 = 0 equationally correct.

Case 2:

=> y - 25 = (x-10)/2, substitute the values x = 20 and y =45,

=> 45 - 25 = (20-10)/2, 20 = 5, equationally incorrect.

=> Option A is incorrect.

Option B:

Case 1:

=> y + 25 = (x+10)*2, substitute the values x = 10 and y = 25,

=> 25 + 25 = (10 + 10)/2, 50 = 40 equationally incorrect.

=> Option B is incorrect.

Option C:

Case 1:

=> y - 25 = (x-10)*2, substitute the values x = 10 and y = 25,

=> 25 - 25 = (10 - 10)/2, 0 = 0 equationally correct.

Case 2:

=> y - 25 = (x-10)*2, substitute the values x = 20 and y =45,

=> 45 - 25 = (20-10)*2, 20 = 20, equationally correct.

=> Option C is correct as it satisfies both the cases.

Option D:

Case 1:

=> y - 10 = (x-25)2, substitute the values x = 10 and y = 25,

=> 25 - 10 = (10 - 25)/2, 15 = -7.5 equationally incorrect.

=> Option D is incorrect.

Therefore, Option C is the correct equation that describes the equation model of the height of the plant.