The problem is asking for an exponential model, which generally takes the form of P = P0 * e^(kt), where P is the final amount, P0 is the initial amount, k is the rate of growth or decay, and t is time.

In this case, we're looking at light intensity at different depths of a lake, so our variables will change a bit. We'll let P be the percentage of light at depth d, P0 be the initial light intensity (which we'll assume is 100% at the surface of the lake), k be the rate of light absorption, and d be the depth.

The problem tells us that 19% of light is absorbed for each 1-meter increase in depth. This means that 81% of the light remains. In decimal form, this is 0.81.

So, our rate of decay k is -0.19 per meter (since the light is decreasing), and our "time" t is the depth d.

Plugging these into our exponential model gives us:

P = 100 * e^(-0.19d)

So, the percentage of light that reaches a depth of d meters is given by P = 100 * e^(-0.19d).

Question

The problem is asking for an exponential model, which generally takes the form of P = P0 * e^(kt), where P is the final amount, P0 is the initial amount, k is the rate of growth or decay, and t is time.

In this case, we're looking at light intensity at different depths of a lake, so our variables will change a bit. We'll let P be the percentage of light at depth d, P0 be the initial light intensity (which we'll assume is 100% at the surface of the lake), k be the rate of light absorption, and d be the depth.

The problem tells us that 19% of light is absorbed for each 1-meter increase in depth. This means that 81% of the light remains. In decimal form, this is 0.81.

So, our rate of decay k is -0.19 per meter (since the light is decreasing), and our "time" t is the depth d.

Plugging these into our exponential model gives us:

P = 100 * e^(-0.19d)

So, the percentage of light that reaches a depth of d meters is given by P = 100 * e^(-0.19d).

Knowee AI · Accepted Answer

The problem is asking for an exponential model, which generally takes the form of P = P0 * e^(kt), where P is the final amount, P0 is the initial amount, k is the rate of growth or decay, and t is time.

In this case, we're looking at light intensity at different depths of a lake, so our variables will change a bit. We'll let P be the percentage of light at depth d, P0 be the initial light intensity (which we'll assume is 100% at the surface of the lake), k be the rate of light absorption, and d be the depth.

The problem tells us that 19% of light is absorbed for each 1-meter increase in depth. This means that 81% of the light remains. In decimal form, this is 0.81.

So, our rate of decay k is -0.19 per meter (since the light is decreasing), and our "time" t is the depth d.

Plugging these into our exponential model gives us:

P = 100 * e^(-0.19d)

So, the percentage of light that reaches a depth of d meters is given by P = 100 * e^(-0.19d).

The intensity of light below the surface of a clear lake depends on many factors. One model shows that 19% of light is absorbed for each 1-meter increase in depth. Find an exponential model, P, for the percentage of light that reaches a depth of d meters.

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