A certain​ houseplant's growth,​ G, in​ inches, varies directly as the number of weeks it has been​ growing, W.

Question

A certain houseplant's growth, G, in inches, varies directly as the number of weeks it has been growing, W.

a. Write an equation that expresses this relationship.

b. This houseplant grows at a rate of about 0.31 inch per week. Substitute 0.31 for k, the constant of variation, in the equation in part (a) and write the equation for the houseplant's growth.

c. Substitute 52 for W to determine the houseplant's growth at the end of one year if it had not been pruned.

Answer 1

The equation may be written as

 

G = kW +G₀

 

Assuming G₀ was the initial length of the plant on day one  

 

k is rate of growth per week

 

W = Number of weeks

 

Assuming G₀ =0

 

G = kW Ans for a

 

G = 0.31  x W    Ans b

 

G = 0.31 x 52 = 16.12 inches at the end of one year      Ans c