Arboriculture

[nycmathguy]

Section 2.2
Question 98

Part (a)

See below.

Part (b)

I think it is safe to say that y is the age of the tree.
Based on the graph on [2, 34], the tree is 55 years old.

You say?

Part (c)

To find the vertex, I must first find t = -b/2a and then evaluate the function at the t-value. Yes?

Part (d)

After completing part (c), I then compare the results to my answer of 55 years for the tree as shown above.

Yes?

 

[MathLover1]

b) according to the graph, the age of the tree when it is growing most rapidly is t=15 (because the slope of the graph is the most steep at that point)

c)
y=-0.009t^2+0.274t+0.458 (this is the first derivative of the function above part a)
vertex is at
(15.2 , 2.5 )

d) estimate was very close, difference is 15.2-15=0.2

 

[nycmathguy]

b) according to the graph, the age of the tree when it is growing most rapidly is t=15 (because the slope of the graph is the most steep at that point)

c)
y=-0.009t^2+0.274t+0.458 (this is the first derivative of the function above part a)
vertex is at
(15.2 , 2.5 )

d) estimate was very close, difference is 15.2-15=0.2

1. Where do you see t = 15 years for the tree?

2. Part (c)

To find the vertex, I must first find t = -b/2a and then evaluate the function at the t-value.

Yes or no?

 

[MathLover1]

1. if you observe your first graph above you see that the curve goes up somewhere around zero to 30, and it is steepest around 15
that is why I estimate t = 15 years for the tree

2. Part (c)

yes, and when you find t = -b/2a (which is x-coordinate of the vertex) , substitute in equation and find y-coordinate of the vertex

 

[nycmathguy]

1. if you observe your first graph above you see that the curve goes up somewhere around zero to 30, and it is steepest around 15
that is why I estimate t = 15 years for the tree

2. Part (c)

yes, and when you find t = -b/2a (which is x-coordinate of the vertex) , substitute in equation and find y-coordinate of the vertex

A much better picture. I think your guess is correct. Section 2.3 tomorrow, Lord willing.

Section 2.3

1. Long Division
2. Synthetic Division