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 − k x , where k Is a constant related to the clarity and other physical properties of the water. The graph shows models for the open ocean. Lake Tahoe, and Lake Erie for data taken under similar conditions. Use these models for Exercises 73-76. The euphoric depth is the depth at which light intensity falls to 1 % of the value at the surface. This depth is of interest to scientists because no appreciable photosynthesis takes place. Find the euphotic depth for the open ocean. Round to the nearest tenth of a meter.
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 − k x , where k Is a constant related to the clarity and other physical properties of the water. The graph shows models for the open ocean. Lake Tahoe, and Lake Erie for data taken under similar conditions. Use these models for Exercises 73-76. The euphoric depth is the depth at which light intensity falls to 1 % of the value at the surface. This depth is of interest to scientists because no appreciable photosynthesis takes place. Find the euphotic depth for the open ocean. Round to the nearest tenth of a meter.
Solution Summary: The author explains that the euphotic depth is the depth at which the light intensity falls to 1% of the value from the surface.
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
−
k
x
,
where k Is a constant related to the clarity and other physical properties of the water. The graph shows models for the open ocean. Lake Tahoe, and Lake Erie for data taken under similar conditions. Use these models for Exercises 73-76.
The euphoric depth is the depth at which light intensity falls to
1
%
of the value at the surface. This depth is of interest to scientists because no appreciable photosynthesis takes place. Find the euphotic depth for the open ocean. Round to the nearest tenth of a meter.
The line graphs in Figure show the percentages of marriages ending in divorce based on the wife’s age at marriage.Here are two mathematical models that approximate the data displayed by the line graphs:In each model, the variable n is the number of years after marriage and the variable d is the percentage of marriages ending in divorce.a. Use the appropriate formula to determine the percentage of marriagesending in divorce after 10 years when the wife is over 25 at the time ofmarriage.b. Use the appropriate line graph in Figure to determine the percentageof marriages ending in divorce after 10 years when the wife is over 25 at the time of marriage.c. Does the value given by the mathematical model underestimate or overestimate the actual percentage of marriages ending in divorce after10 years as shown by the graph? By how much?
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