SOLUTION: The function f(x)=20(0.975)^x models the percentage of the surface sunlight, f(x), that reaches a depth of x feet beneath the surface of the ocean. Use the function f(x) to algebra

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Question 1188014: The function f(x)=20(0.975)^x models the percentage of the surface sunlight, f(x), that reaches a depth of x feet beneath the surface of the ocean. Use the function f(x) to algebraically determine the depth, to the nearest hundredths of the foot, there is a 10% of surface sunlight. Use logarithms.
Answer by ikleyn(53937) (Show Source):
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The function f(x)=20(0.975)^x models the percentage of the surface sunlight, f(x),
that reaches a depth of x feet beneath the surface of the ocean.
Use the function f(x) to algebraically determine the depth, to the nearest hundredths
of the foot, there is a 10% of surface sunlight. Use logarithms.
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According to the function, at the ocean surface x = 0, the intencity of sunlight is 20 units. 10% os 20 units is 2 units, so we write this equation 2 = , divide by 20 both sides = 0.1 = take logarithm base 10 of both sides log(0.1) = x*log(0.975) -1 = x*log(0.975) anf get x = = 90.95 (rounded as requested). ANSWER. This depth is 90.95 ft.

Solved.