Question

Owlet talons Let L (t) equal the average length (in mm) of the middle talon on an Indian spotted owlet that is t weeks old, as shown in the figure.<IMAGE>
a. Estimate L' (1.5) and state the physical meaning of this quantity.

Accepted Answer

Step 1: Understand the function L(t) which represents the average length of the middle talon of an Indian spotted owlet at t weeks old. The derivative L'(t) represents the rate of change of the talon length with respect to time. Step 2: To estimate L'(1.5), we need to find the slope of the tangent line to the curve L(t) at t = 1.5. This can be done by finding two points on the curve close to t = 1.5 and calculating the average rate of change between them. Step 3: Choose two points on the curve, say (t1, L(t1)) and (t2, L(t2)), where t1 is slightly less than 1.5 and t2 is slightly more than 1.5. For example, you might choose t1 = 1 and t2 = 2. Step 4: Calculate the average rate of change between these two points using the formula: $$ \frac{L(t2) - L(t1)}{t2 - t1} . $$This will give an approximation of L'(1.5). Step 5: Interpret the physical meaning of L'(1.5). It represents the rate at which the length of the middle talon is growing at 1.5 weeks. A positive value indicates growth, while a negative value would indicate a decrease in length.

Owlet talons Let L (t) equal the average length (in mm) of the middle talon on an Indian spotted owlet that is t weeks old, as shown in the figure.<IMAGE>
a. Estimate L' (1.5) and state the physical meaning of this quantity.

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Key Concepts

Derivative

Average Length Function

Physical Interpretation

Owlet talons Let L (t) equal the average length (in mm) of the middle talon on an Indian spotted owlet that is t weeks old, as shown in the figure.<IMAGE>a. Estimate L' (1.5) and state the physical meaning of this quantity.