Question

During the first few years of a tree's life, its growth rate is linear. For example, an oak tree grows at a rate of 1.5 feet per year for the first twelve years. Mostafa plants a maple tree in his backyard and measures its height at 4 feet. Two years later, Mostafa measures the tree again and finds that its height is now 6.5 feet. Which statement is correct given this information?

Answer 1

Mostafa's maple tree grows at a slower yearly rate than an oak tree.

Explanation:

Given that:

An oak tree grows at a rate of 1.5 feet per year for twelve years;

After 12 year; the oak tree will be = 12 × 1.5 = 18 feet per year.

Now; we are being told that Mostafa plants a maple tree at his backyard and measures its height at 4 feet.

i.e x years = 4 ft

two years later ; it height is now 6.5 ft

thus;

x year = 4 ft

x + 2 = 6.5 ft

`6.5 * x = (x+2)4\\ \\ 6.5 x = 4x + 8\\ \\ 6.5x-4x = 8\\ \\ 2.5x = 8\\ \\ x = (8)/(2.5)\\ \\ x = 3.2`

Thus ; Mostafa first measured the height of the tree when it is 4 ft at the age year of 3.2

So;

if 3.2 year = 4 ft

1 year = x

x =
`(4 *1 )/(3.2)`

x = 1.25 ft

So if an oak tree grows at the rate of 1.5 ft in a year.

Then, Mostafa's maple tree grows at the rate of 1.25 ft in a year.

From the given information in the diagram attached below; we can infer that :

Mostafa's maple tree grows at a slower yearly rate than an oak tree.