The light intensity I (in lumens) at a depth of x feet in Lake Elizabeth is given by the formula log = - 0.025x, 12 a. Find the light intensity at a depth of 30 feet. b. At what depth is the light intensity 6 lumens? a. The light intensity at a depth of 30 feet is lumens. (Do not round until the final answer. Then round to three decimal places as needed.)
The light intensity I (in lumens) at a depth of x feet in Lake Elizabeth is given by the formula log = - 0.025x, 12 a. Find the light intensity at a depth of 30 feet. b. At what depth is the light intensity 6 lumens? a. The light intensity at a depth of 30 feet is lumens. (Do not round until the final answer. Then round to three decimal places as needed.)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
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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![### Problem 4.4.107
The light intensity \( I \) (in lumens) at a depth of \( x \) feet in Lake Elizabeth is given by the formula:
\[ \log \left( \frac{I}{12} \right) = -0.025x \]
#### Questions:
a. Find the light intensity at a depth of 30 feet.
b. At what depth is the light intensity 6 lumens?
#### Solutions:
a. The light intensity at a depth of 30 feet is \( \underline{\hspace{2cm}} \) lumens.
*(Do not round until the final answer. Then round to three decimal places as needed.)*
This educational website section describes the logarithmic relation between light intensity \( I \) at various depths \( x \) in Lake Elizabeth. The given formula shows how light diminishes exponentially with increasing depth. The problem includes two parts: calculating the light intensity at a specific depth and determining the depth at a given light intensity. Complete each part by applying logarithmic and algebraic operations, ensuring to round the final answer to three decimal places for accuracy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd446bb1a-5a9f-42c0-b85c-8f8e02c8d979%2F37c8ab9f-cd00-4cea-92ca-317565314050%2F3i0donh_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 4.4.107
The light intensity \( I \) (in lumens) at a depth of \( x \) feet in Lake Elizabeth is given by the formula:
\[ \log \left( \frac{I}{12} \right) = -0.025x \]
#### Questions:
a. Find the light intensity at a depth of 30 feet.
b. At what depth is the light intensity 6 lumens?
#### Solutions:
a. The light intensity at a depth of 30 feet is \( \underline{\hspace{2cm}} \) lumens.
*(Do not round until the final answer. Then round to three decimal places as needed.)*
This educational website section describes the logarithmic relation between light intensity \( I \) at various depths \( x \) in Lake Elizabeth. The given formula shows how light diminishes exponentially with increasing depth. The problem includes two parts: calculating the light intensity at a specific depth and determining the depth at a given light intensity. Complete each part by applying logarithmic and algebraic operations, ensuring to round the final answer to three decimal places for accuracy.
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