A plant nursery is growing a tree

Question

A plant nursery is growing a tree that is 3 ft tall and grows at an average rate of 1 ft per year. Another tree at the nursery is 4 ft tall and grows at an average rate of 0.5 ft per year. After how many years will the trees be the same height?

Answer 1

If we let h represent the tree height, and y the number of years, we can write equations to represent the trees' heights as a function of the number of years.

 

First tree:  h₁ = y + 3     (the height of the tree is 1 foot per year plus the 3 feet it started at)

 

Second tree:  h₂ = 0.5y + 4   (the height of the tree is 0.5 feet per year plus the 4 feet it started at)

 

Their heights will be equal when

    

    y + 3  =  0.5y  +  4

 

Now we need to solve this equation:

 

    y + 3  =  0.5y  +  4

 

         -3  =          -   3

   -------------------------

      y      =  0.5y  +  1

 

 -0.5y     =  -0.5y

   -------------------------

  0.5y     =               1

 

0.5y/0.5 =              1/0.5

 

     y       =              2 

 

Do you know how tall the trees are after 2 years?

 

Answer 2

Hi Alana,

 

Let x represent the number of years the trees grow. Let y represent the height of the trees after x number of years. Then the height of the first tree would be  y = 3 + 1x and the other tree's height would be  y = 4 + 0.5x  To determine how long it would take for the trees to be the same height, simply set the two expressions for the tree heights equal to each other.

                                             3 + 1x = 4 + 0.5x and solve for x.

                                                 0.5x = 1

                                                     x = 2 years

Answer 3

3+1+1=5

4+.5+.5=5

 

If you add the growth for two years to each tree, you get a tree 5 feet tall. Therefore, the answer is 2 years.

 

For dates longer than 2 years, you would obviously want to use a formula for each of the trees. Those would be

y = 1x + 3 and y = 0.5x + 4. Then you would solve for x.