To predict the saturated thickness in 2015, we need to analyze the given data and establish a trend for the rate at which the thickness is decreasing over the years. Here is a step-by-step breakdown of how to make this prediction:
### Step 1: Gather the Data
From the table, we have the following years and corresponding saturated thicknesses:
- 1975: 32.77 m
- 1980: 29.11 m
- 1985: 25.68 m
- 1990: 22.48 m
- 1995: 19.43 m
- 2000: 16.84 m
- 2005: 14.55 m
- 2010: 12.27 m
### Step 2: Calculate the Rate of Change for Each Interval
Calculate the rate of change of the saturated thickness between each consecutive pair of years.
- Between 1975 and 1980:
[tex]\[
\frac{32.77 - 29.11}{1980 - 1975} = 0.732 \, \text{meters per year}
\][/tex]
- Between 1980 and 1985:
[tex]\[
\frac{29.11 - 25.68}{1985 - 1980} = 0.686 \, \text{meters per year}
\][/tex]
- Between 1985 and 1990:
[tex]\[
\frac{25.68 - 22.48}{1990 - 1985} = 0.64 \, \text{meters per year}
\][/tex]
- Between 1990 and 1995:
[tex]\[
\frac{22.48 - 19.43}{1995 - 1990} = 0.61 \, \text{meters per year}
\][/tex]
- Between 1995 and 2000:
[tex]\[
\frac{19.43 - 16.84}{2000 - 1995} = 0.518 \, \text{meters per year}
\][/tex]
- Between 2000 and 2005:
[tex]\[
\frac{16.84 - 14.55}{2005 - 2000} = 0.458 \, \text{meters per year}
\][/tex]
- Between 2005 and 2010:
[tex]\[
\frac{14.55 - 12.27}{2010 - 2005} = 0.456 \, \text{meters per year}
\][/tex]
The rates of change in saturated thickness between each consecutive period are:
[tex]\[ [0.732, 0.686, 0.64, 0.61, 0.518, 0.458, 0.456] \][/tex]
### Step 3: Calculate the Average Rate of Change
Now, we compute the average of these rates:
[tex]\[
\frac{0.732 + 0.686 + 0.64 + 0.61 + 0.518 + 0.458 + 0.456}{7} = 0.586 \, \text{meters per year}
\][/tex]
### Step 4: Predict the Saturated Thickness in 2015
With the average rate of change we computed, we can predict the thickness in 2015. In 2010, the thickness was 12.27 meters. The number of years from 2010 to 2015 is 5 years. Therefore:
[tex]\[
\text{Predicted thickness in 2015} = 12.27 - (0.586 \times 5) = 12.27 - 2.93 = 9.34 \, \text{meters}
\][/tex]
### Conclusion
Based on the calculated value, the saturated thickness in 2015 will be around 9.34 meters.
Thus, the correct answer to the question is:
"It will be near 10 meters."
