Question

7. The height of a sunflower plant varies directly with its age. Once it has sprouted from the ground, when a sunflower is 2 week old, it is 38 centimeters tall. When it is 6 weeks old, it is 114 centimeters tall. How tall is a sunflower plant that is 3 1/2 weeks old?

Answer 1

The sunflower plant is 66.5 cm at 3 1/2 weeks old.

Answer 2

66.5 centimeters.

Explanation:

We have been given that the height of a sunflower plant varies directly with its age.

Since a directly proportional equation is in form:
`y=kx`, where k is constant of proportionality.

We are told that when a sunflower is 2 week old, it is 38 centimeters tall. Let us find constant of proportionality with given information.

`38=k\cdot 2`

`(38)/(2)=k`

`19=k`

We are also told that when sunflower is 6 weeks old, it is 114 centimeters tall.

`114=k\cdot 6`

`(114)/(6)=k`

`19=k`

We can see that constant of proportionality is 19. Let us substitute k=19 and x= 3.5 in our proportional equation to find the height of plant after 3.5 weeks.

`y=19\cdot 3.5`

`y=66.5`

Therefore, the sunflower plant will be 66.5 centimeters tall after 3.5 weeks.