Question

A mountain in Benton County is eroding and losing elevation at a rate of 1% every millennium. If the current elevation is 953 meters, how tall will the mountain be in 7 millennia?
If necessary, round your answer to the nearest whole number.
meters

Answer 1

To find the elevation of the mountain after 7 millennia, we first need to determine the rate of erosion. The mountain is losing elevation at a rate of 1% per millennium, which means it retains 99% of its elevation each millennium.

The formula to calculate the remaining height after multiple periods of erosion is:

\[
\text{Height after } n \text{ millennia} = \text{Initial Height} \times (1 - \text{Rate of Erosion})^n
\]

In this case:
- Initial Height = 953 meters
- Rate of Erosion = 1% = 0.01
- Remaining height after each millennium = 1 - 0.01 = 0.99
- \( n = 7 \)

Now we can substitute the values into the formula:

\[
\text{Height after 7 millennia} = 953 \times (0.99)^7
\]

Calculating \( (0.99)^7 \):

\[
(0.99)^7 \approx 0.932065
\]

Now we multiply this by the initial height:

\[
\text{Height after 7 millennia} \approx 953 \times 0.932065 \approx 887.04
\]

Rounding to the nearest whole number:

\[
\text{Height after 7 millennia} \approx 887 \text{ meters}
\]

Therefore, the mountain will be approximately **887 meters** tall in 7 millennia.