Answer:
66.5 centimeters.
Step-by-step 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: [tex]y=kx[/tex], 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.
[tex]38=k\cdot 2[/tex]
[tex]\frac{38}{2}=k[/tex]
[tex]19=k[/tex]
We are also told that when sunflower is 6 weeks old, it is 114 centimeters tall.
[tex]114=k\cdot 6[/tex]
[tex]\frac{114}{6}=k[/tex]
[tex]19=k[/tex]
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.
[tex]y=19\cdot 3.5[/tex]
[tex]y=66.5[/tex]
Therefore, the sunflower plant will be 66.5 centimeters tall after 3.5 weeks.
