The intensity of light decreases by 4% for each meter that it descends below the surface of the water. At what depth is the intensity of light only 20% of that at the surface?

I = 1 (.96)^m

.20 = .96^m
using logs

m = log .2/log .96 = appr 39.4

it would take about 39.4 m

A colony of bees doubles in population every 5 weeks. how long does it tak for the population to triple?

Log(3/1)/Log(2)=1.58

1.58x5=7.9 weeks

Why did the light bulb dive into the water? It wanted to see if it could make a splash with its brightness! Now, let's dive into your question.

If we start at the surface as our reference point with an intensity of 100%, and it decreases by 4% for every meter, we can set up an equation to find the depth at which the intensity reaches 20%.

Let's call the depth d in meters. So, the equation would be:

100% - 4% * d = 20%

Now, let's solve for d:

100% - 20% = 4% * d
80% = 0.04d
d = 80% / 0.04
d = 2000 meters

So, at a depth of 2000 meters, the intensity of light would be only 20% of that at the surface. Just remember to bring some extra waterproof sunscreen for your light bulbs when you go that deep!

To find the depth at which the intensity of light is only 20% of that at the surface, we can use the concept of exponential decay.

Let's assume that the depth is "d" meters below the surface. According to the problem, the intensity of light decreases by 4% for each meter it descends.

We can express the decrease in intensity as a decimal fraction, which in this case would be 0.04.

Using the formula for exponential decay, we can find the expression for the intensity of light at a depth of "d" meters:

Intensity at depth d = Intensity at the surface * (1 - decrease rate)^(depth in meters)

Substituting the given values:

0.20 = 1 * (1 - 0.04)^d

Simplifying further:

0.20 = 0.96^d

Now, to solve for "d", we can take the logarithm of both sides of the equation. Let's take the natural logarithm (ln) to simplify the expression:

ln(0.20) = d * ln(0.96)

Now, we can solve for "d" by dividing both sides of the equation by ln(0.96):

d = ln(0.20) / ln(0.96)

Using a calculator, we can find the approximate value of "d" to be approximately 13.86 meters.

Therefore, the intensity of light is only 20% of that at the surface at a depth of approximately 13.86 meters.