Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light P (in decimal form) at a depth of x meters is given by P = e-kx, where k is a constant related to the clarity and other physical properties of the water. The model for a particular lake is P = e-0.1284x. Determine the depth at which the light intensity is 80% of the value from the surface for this lake. Round to the nearest tenth of a meter.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 30E: The table shows the mid-year populations (in millions) of five countries in 2015 and the projected...
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Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light P (in decimal form) at a depth of x meters is given by P = e-kx, where k is a constant related to the clarity and other physical properties of the water. The model for a particular lake is P = e-0.1284x. Determine the depth at which the light intensity is 80% of the value from the surface for this lake. Round to the nearest tenth of a meter.

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