Question

a cliff overlooking dover lake is experiencing erosion, losing elevation at a rate of 5% every millennium. the cliff's current elevation is 1,519 meters. what will its elevation be in 10 millennia?

Answer 1

Using exponential decay, the elevation of the cliff overlooking Dover Lake after 10 millennia, with a 5% loss per millennium, would be approximately 908.82 meters.

Step-by-step explanation:

To find the cliff's elevation after 10 millennia, we use the concept of exponential decay, which describes the process of losing a fixed percentage over a given time period. In one millennium, the cliff loses 5% of its elevation, so the decay rate per millennium is 0.95 (100% - 5%).

Using the formula for exponential decay, elevation after t millennia = initial elevation × (decay rate)^t, we can calculate the elevation after 10 millennia.

Initial elevation: 1,519 meters
Decay rate: 0.95 (95% remains after one millennium)
Time (t): 10 millennia.

Therefore, the elevation after 10 millennia is:

1,519 meters × (0.95)^10 ≈ 1,519 meters × 0.59874 ≈ 908.82 meters.

After 10 millennia, the cliff overlooking Dover Lake is projected to have an elevation of approximately 908.82 meters.