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icang [17]
3 years ago
5

The height of a tree in feet over x years is modeled by the function f(x). f(x)=301+29e−0.5x which statements are true about the

growth of the tree? select each correct answer. the tree's maximum height is limited to 30 ft. the tree is initially 2 ft tall. between the 5th and 7th years, the tree grows approximately 7 ft. after growing 15 ft, the tree's rate of growth decreases.

Mathematics
2 answers:
Karo-lina-s [1.5K]3 years ago
4 0
Given this equation:

f(x)=301+29^{-0.5x}

That represents t<span>he height of a tree in feet over (x) years. Let's analyze each statement according to figure 1 that shows the graph of this equation.
</span>
The tree's maximum height is limited to 30 ft.

As shown in figure below, the tree is not limited, so this statement is false.

<span>The tree is initially 2 ft tall

The tree was planted in x = 0, so evaluating the function for this value, we have:

</span>f(0)=301+29^{-0.5(0)}=301+1=302ft
<span>
<span>So, the tree is initially \boxed{302ft} tall.
</span>
Therefore this statement is false.

</span>Between the 5th and 7th years, the tree grows approximately 7 ft.
<span>
if x = 5 then:

</span>f(5)=301+29^{-0.5(5)}=301ft<span>

</span>if x = 7 then:

f(7)=301+29e^{0.5(7)}=301ft

So, between the 5th and 7th years the height of the tree remains constant
:
\Delta=f(7)-f(5)=301-301=0ft

This is also a false statement.

<span>After growing 15 ft, the tree's rate of growth decreases.</span>

It is reasonable to think that the height of this tree finally will be 301ft. Why? well, if x grows without bound, then the term 29^{-\infty} approaches zero.

Therefore this statement is also false.

Conclusion: After being planted this tree won't grow. 


Veseljchak [2.6K]3 years ago
3 0

Answer:


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

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

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



These are the correct answer i just took the TEST!!


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