Answer :
Final answer:
After 7 millennia, the height of the mountain, currently at 953 meters and eroding at a rate of 1% per millennium, will be approximately 888 meters when calculated using the exponential decay formula.
Explanation:
Exponential Decay Problem
In this problem, we are dealing with exponential decay, which occurs when a quantity decreases at a constant percentage rate. Let's calculate the height of the mountain after 7 millennia.
The current elevation of the mountain is 953 meters, and it is losing elevation at a rate of 1% per millennium. To find the elevation after 7 millennia, we can use the formula for exponential decay:
- Final Amount (A) = Initial Amount (P) × (1 - r)^t
Where:
- A = future amount (elevation after t millennia)
- P = initial amount (current elevation)
- r = rate of decay (as a decimal)
- t = time (in millennia)
In our case, this translates to:
- P = 953
- r = 0.01 (1% as a decimal)
- t = 7
Now, plugging in the values:
- A = 953 × (1 - 0.01)^7
- A = 953 × (0.99)^7
- A ≈ 953 × 0.932065
- A ≈ 887.63
Rounding to the nearest whole number, the mountain's height in 7 millennia will be approximately 888 meters.
Learn more about Exponential decay here:
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