Question

8. The diameter, in meters, of a tree trunk is modeled by the functiond(h)= 1.31 Ž, where h is the height of the tree in meters. What is theapproximate diameter of a 50 meter tall tree?h=50110 cmАB.230 cm15C. 460 cmdC5037 13.6507)D. 520 cm

Answer 1

Answer:

The diameter of the tree is 46000 cm

Explanations:

The diameter of the tree trunk is modeled by the function:

`d(h)=1.3h^{(3)/(2)}`

Where h represents the height of the tree in meters

When h = 50 m

Substitute h = 50 m into the given equation

`\begin{gathered} d(50)=1.3(50)^{(3)/(2)} \\ d(50)=1.3(50)^(1.5) \\ d(50)\text{ = 1.3}*353.55 \\ d(50)\text{ = }459.615\text{ m} \\ d(50)\text{ = 460 m} \end{gathered}`

The diameter of the tree is 460 m

To convert the diameter to cm, multiply it by 100

d = 460 x 100

d = 46000 cm

The diameter of the tree is 46000 cm