Solve for x, Pre Cal 12: chap 8

Solve for x in each of the following equations At least 2 of the 4 must be solved algebraically. When solving graphically, sketch or paste a digital image of the graph you used to solve for the question.

1. e^(2x)-e^(x)-12=0
2. 2(5^(x+2))=5(2^(x+5))
3. The percentage of sunlight that penetrates the water of the ocean decays exponentially with depth and can be described by the equation L(x)=100e^((k)x) where L is the % of sunlight, x is the depth of water in metres, and k is a constant that varied depending upon water conditions (k=-0.2 for clear water).
   1. Assuming the water is clear, what percentage of the sun’s light penetrates water at 9.0m depth?
   2. How deep is clear water when only 5% of the sun’s light reaches it?
4. A 200-g sample of a radioactive substance is placed in a chamber to be tested. After 3 h have passed only 140 g of the sample remains.
   1. Determine the half-life of this substance, to the nearest hundredth of an hour.
   2. How much of the substance will remain after 1.5 days?