Question

Suppose a vine maple grows in height linearly. Four weeks after it is planted it stands 5 inches, and after eight weeks it is 7 inches tall. Write an equation that models the growth, in inches, of the vine maple as a function of time, in weeks.

Answer 1

Given

A plant which takes four weeks to grow 5 inches and after eight weeks it is 7 inches tall

To find

Equation that models the growth, in inches, of the vine maple as a function of time, in weeks

Solution

Let $x$ axis represent the time in weeks and $y$ axis represent the growth of the plant.

So, the points will be $(4,5)$ and $(8,7)$

Slope of the line that models the linear increase in height is

$m=\dfrac{\Delta y}{\Delta x}\\\Rightarrow m=\dfrac{7-5}{8-4}\\\Rightarrow m=\dfrac{2}{4}\\\Rightarrow m=\dfrac{1}{2}$

The equation of the line is given by

$y-5=\dfrac{1}{2}(x-4)\\\Rightarrow y=\dfrac{1}{2}x-2+5\\\Rightarrow y=\dfrac{1}{2}x+3$

The equation that models the growth, is $y=\dfrac{1}{2}x+3$