**Title: Calculating the Width of Growth Spirals in Seashells**The width $ w $ (in millimeters) of successive growth spirals of the sea shell *Catapulus voluto*, shown in the illustration below, is given by the exponential function:\[ w = 1.54e^{0.503n} \]where $ n $ is the spiral number. Find the width, to the nearest tenth of a millimeter, of the **third spiral**.[ Illustration of a seashell with labeled spirals ]In the illustration, the spirals are labeled with numbers 1 through 6. The width $ w $ of the spirals is indicated by a horizontal arrow pointing to the third spiral. The equation provided can be used to calculate the width for any given spiral number $ n $ by substituting $ n $ into the formula.Input your answer in the box provided:\[ \_\_\_\_\_\_ \text{ mm} \]To find the width of the third spiral, substitute $ n = 3 $ into the formula and solve.**Note:**- Ensure to use a calculator for the computation involving the exponential function.- Round your answer to the nearest tenth of a millimeter.

We need to find the width of third spiral.

The width w (in millimeters) of successive growth spirals of the sea shell Catapulus voluto, shown in the illustration below, is given by the exponential function w = 1.54e0.503n where n is the spiral number. Find the width, to the nearest tenth of a millimeter, of the third spiral. mm 5 4 321 W

The width w (in millimeters) of successive growth spirals of the sea shell Catapulus voluto, shown in the illustration below, is given by the exponential function w = 1.54e0.503n where n is the spiral number. Find the width, to the nearest tenth of a millimeter, of the third spiral. mm 5 4 321 W

Algebra and Trigonometry (6th Edition)

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Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

**Title: Calculating the Width of Growth Spirals in Seashells**

The width $ w $ (in millimeters) of successive growth spirals of the sea shell *Catapulus voluto*, shown in the illustration below, is given by the exponential function:

\[ w = 1.54e^{0.503n} \]

where $ n $ is the spiral number. Find the width, to the nearest tenth of a millimeter, of the **third spiral**.

[ Illustration of a seashell with labeled spirals ]

In the illustration, the spirals are labeled with numbers 1 through 6. The width $ w $ of the spirals is indicated by a horizontal arrow pointing to the third spiral. The equation provided can be used to calculate the width for any given spiral number $ n $ by substituting $ n $ into the formula.

Input your answer in the box provided:
\[ \_\_\_\_\_\_ \text{ mm} \]

To find the width of the third spiral, substitute $ n = 3 $ into the formula and solve.

**Note:**
- Ensure to use a calculator for the computation involving the exponential function.
- Round your answer to the nearest tenth of a millimeter.

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