Question

A gardener transplanted a plant from an indoor pot to an outdoor garden. After 30 days, the plant's height was 18 centimeters. After 90 days, it was 29 centimeters. Write an equation to represent the plants growth where the x is the days and the y is the height of the plant.

Answer 1

Let x is the days and the y is the height of the plant.

Let the change between x and y is linear.

So, the relation between x and y will take the form ⇒ y = ax + b

where a and b are constants.

At x = 30 ⇒ y = 18 ⇒⇒⇒ ∴ 18 = 30 a + b → (1)

At x = 90 ⇒ y = 29 ⇒⇒⇒ ∴ 29 = 90 a + b → (2)

solve (1) and (2) to find a and b

subtract (1) from (2)

∴ 11 = 60 a ⇒⇒⇒ ∴ a = 11/60

substitute at (1) ⇒⇒⇒ ∴ b = 25/2 = 12.5

So, the equation which represents the plants growth is

∴ y = (11/60) x + 12.5

Explanation:

Answer 2

Let x is the days and the y is the height of the plant.

Let the change between x and y is linear.

So, the relation between x and y will take the form ⇒ y = ax + b

where a and b are constants.

At x = 30 ⇒ y = 18 ⇒⇒⇒ ∴ 18 = 30 a + b → (1)

At x = 90 ⇒ y = 29 ⇒⇒⇒ ∴ 29 = 90 a + b → (2)

solve (1) and (2) to find a and b

subtract (1) from (2)

∴ 11 = 60 a ⇒⇒⇒ ∴ a = 11/60

substitute at (1) ⇒⇒⇒ ∴ b = 25/2 = 12.5

So, the equation which represents the plants growth is

∴ y = (11/60) x + 12.5