Question

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?


Select each correct answer.


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

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

The tree is initially 2 ft tall.

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

Answer 1

If e-the initial hight of the tree, and the function imply some brackets like

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

for every

`0.5x > 29e + 1`

the rate of growth is negative, the maximum growth per unit of time would be 30ft

If

`x \geqslant 1`

then

`29e < - 0.5`

so the tree couldn't be 2ft tall initially

if the brackets are something like

f(x)=30:(1+29e)-0.5x then the results may differ