Answer :
Answer:
Step-by-step explanation:
We can find the number of years (x) it takes for the tree to grow to 30 feet (y) by solving the model equation for x. Here's how:
Set the model equation equal to 30 (desired height):
y = 2.062 + 7.695 ln(x) = 30
Isolate ln(x):
Subtract 2.062 from both sides:
ln(x) = (30 - 2.062) / 7.695 ≈ 3.712
Solve for x (find the anti-logarithm):
Important: We can't directly isolate x by dividing by ln because logarithms don't work like that. Instead, we need to take the exponent of both sides with base e (Euler's number, approximately 2.718). This operation is called the anti-logarithm and is often denoted by exp or e raised to the power of.
Formula: e^(ln(x)) = x (where e is Euler's number)
Apply the anti-logarithm (exponent with base e) to both sides:
e^(ln(x)) = e^(3.712) ≈ 41.3 years (rounded to nearest tenth)
Interpretation:
According to the model, it will take approximately 41.3 years for the tree to grow to 30 feet tall.
Note: It's important to remember that this is an estimate based on the provided logarithmic regression model. The actual growth rate of a tree can be influenced by various factors not considered in the model.
