Question

When purchased, the height of a Japanese maple sapling is 14 inches. The tree is expected to grow 2.5 inches each month. Which function models the relationship between the height of the tree f(m) and the number of m months of growth? A) f(m) = 2.5m B) f(m) = 2.5m + 14 C) f(m) = 14m + 2.5 D) f(m) = 2.5m − 14

Answer 1

Explanation:

The initial height of a Japanese maple sapling is 14 inches.

The tree is expected to grow 2.5 inches each month. This increase in height is linear, thus it is in arithmetic progression.

The expression for arithmetic progression is

Tn = a + (n-1)d

Where a = the first term of the series

d = common difference

Tn is the nth term of the series

n = the number of terms.

From the information given

a = 14 inches because it is the initial height of the tree

d = 2.5 because it is the difference in height between 2 consecutive months

n = m( number of months)

Tn = f(m)

function models the relationship between the height of the tree f(m) and the number of m months of growth will be

f(m) = 14 + 2.5(m-1)