Question

A vine maple grows fast when it is planted under the cover of cedar trees. One month after it is planted it has grown 9 inches, and after eight weeks it had grown 14 inches.

Write an equation that models the growth, in inches, of the vine maple as a function of time, in weeks

Answer 1

`y=(5)/(4) x+4`

Explanation:

Using y = mx+c

m=
`(y^(2)-y^(2))/(x^(2)-x^(1))`

m=
`(14-9)/(8-4)`

m=
`(5)/(4)`

c=y-intercept

The question says that at 8 weeks the maple had grown 14 inches

By using y=mx+c we can find the y-intercept using one of the points as the x and y values and by using the slope

`14=8*(5)/(4) +c`

14=10+c

14-10=10+c-10

4=c

y-intercept = 4

Therefore the full equation is

`y=(5)/(4) x+4`