Question 1188014
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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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<pre>
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 = {{{20*0.975^x}}},


divide by 20 both sides


    {{{2/20}}} = {{{0.975^x}}}

      0.1 = {{{0.975^x}}}


take logarithm base 10 of both sides


    log(0.1) = x*log(0.975)

      -1     = x*log(0.975)


anf get

      x     =  {{{(-1)/log(0.975)}}} = 90.95   (rounded as requested).


<U>ANSWER</U>.  This depth is  90.95 ft.
</pre>

Solved.