Question

Depth and light intensity measured in Thunder Lake As you move deeper into any body of water, sunlight is absorbed by water and other particles in solution and the area grows darker. The goal of this project is to determine how deep you would be able to operate a device to study the pollution in Thunder Lake.

dept (m)	light intensity (lumens)
1	14.7
2	11.9
3	9.5
4	6.1

1) Create a scatterplot of the data and find an exponential function to model the data.

2) What does x=0 mean in the context of this problem?

3) What does the coefficient outside the exponential mean in the context of this problem?

4) An instrument you designed to study pollution in the lake requires a light intensity of at least 0.1 lumen to function properly. According to the model, how deep would you be able to lower this instrument into the lake without an additional light source?

5) If you needed to take multiple measurements in the lake, what additional information would you need about the data and what other factors would you need to consider that would affect the maximum depth or need for additional light?

Answer 1

(1)

Intensity = 20.532e^-0.286x is the equation of exponential fit.

(2)

x = 0 means at the surface of the water of the lake.

(3) coefficient outside the exponential is the intensity at the surface of the lake

4) An instrument you designed to study pollution in the lake requires a light intensity of at least 0.1 lumen to function properly.

y = 1= 20.532e^-0.286x

x = ln(20.532) / 0.286 = 10.566 lumens