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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.