algebra 2 high school

Question

The amount of sunlight penetrating a lakes surface is exponentially related to the depth of the water. In a particular lake the reduction is 18% per foot of depth.

1. write an equation representing the percentage of sunlight reaching x feet below surface.

2. A particular aquatic plant needs 25% of the original sun to grow. Can it grow at a depth of 5 feet in this lake?

Answer 1

For a depth of x feet...

 

With sunlight S as a function of depth x

S(x) = S₀(.82)^x

because for each foot of depth the sunlight

is 82% of the previous depth.  S₀ is the

amount of sunlight at the surface.

 

S(5) = 1(.82)⁵ = 0.37 = 37%

 

Note:  The original amount at surface is 100%.

As a number for the equation 100% = 100/100=1

 

Since 37% is greater than 25% the plant can grow

at a depth of 5 feet.

Answer 2

So, Ashley, if we take away 18%, we are left with 82%, right?

 

So, after the first foot, 82% is reaching. At foot 2, .82(.82) = .67 = 67% is reaching, etc.

 

Our equation is r(x) = .82^x.

 

I bet you can get part 2!