In the model lnh = -1.2 + 1.4(ln c), if a tree has a circumference of 60 inches, what is the height estimate of the tree according to this model?

In the model lnh = -1.2 + 1.4(ln c), if a tree has a circumference of 60 inches, what is the height estimate of the tree according to this model?

• A. 75 inches
• B. 85 inches
• C. 93 inches
• D. 100 inches

Answer: (C)

To estimate the height of the tree using the provided model, we start with the equation given: \( lnh = -1.2 + 1.4(ln c) \) Here, \( h \) represents the height of the tree and \( c \) represents the circumference. To find the height estimate for a tree with a circumference of 60 inches, we first need to calculate \( ln c \): 1. Calculate \( ln(60) \). This is approximately \( 4.094 \) (using a scientific calculator). 2. Substitute this value into the model: \( lnh = -1.2 + 1.4(4.094) \) 3. Perform the multiplication: \( 1.4 \times 4.094 \approx 5.731 \) 4. Now, add this result to \(-1.2\): \( lnh \approx -1.2 + 5.731 = 4.531 \) 5. To find \( h \), we must take the exponential of both sides: \( h = e^{4.531} \), which is approximately \( 93 \) inches. Thus, the correct estimate

To estimate the height of the tree using the provided model, we start with the equation given:

( lnh = -1.2 + 1.4(ln c) )

Here, ( h ) represents the height of the tree and ( c ) represents the circumference. To find the height estimate for a tree with a circumference of 60 inches, we first need to calculate ( ln c ):

1. Calculate ( ln(60) ). This is approximately ( 4.094 ) (using a scientific calculator).

2. Substitute this value into the model:

( lnh = -1.2 + 1.4(4.094) )

3. Perform the multiplication:

( 1.4 \times 4.094 \approx 5.731 )

4. Now, add this result to (-1.2):

( lnh \approx -1.2 + 5.731 = 4.531 )

5. To find ( h ), we must take the exponential of both sides:

( h = e^{4.531} ), which is approximately ( 93 ) inches.

Thus, the correct estimate