The height of a tree in feet over x years is modeled by the function f (x).

f (x) = 30/1+29e^-0.5x

which statements are true about the growth of the tree? Check all that apply.

-After growing 15 ft, the tree's rate of growth decreases.

-The tree is initially 2 ft tall.

-Between the 5th and 7th years, the tree grows approximately 7 ft.

-The tree's maximum height is limited to 30 ft.

Question

Mathematics

Elisha Martinez

11 April, 12:56

The height of a tree in feet over x years is modeled by the function f (x).

f (x) = 30/1+29e^-0.5x

which statements are true about the growth of the tree? Check all that apply.

-After growing 15 ft, the tree's rate of growth decreases.

-The tree is initially 2 ft tall.

-Between the 5th and 7th years, the tree grows approximately 7 ft.

-The tree's maximum height is limited to 30 ft.

+3

Answers (1)

Know the Answer?

Leslie Cowan · Answer 1

The following statements are true:

The tree grows approximately 7 feet between years 5 and 7;

the tree stops growing at around 30 feet

In graphing the function, we see that the initial value, when x = 0, is 1 ft, not 2.

Additionally, we can see the values as the height increases; when the tree hits 15 feet, it continues to grow at around 1.5 feet every 0.4 years until it hits around 25 feet tall. Then it begins to slow down.