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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.

Answer :

Final answer:

The mountain's height after 7 millennia, considering a 1% erosion rate per millennium, would be about 888 meters when rounded to the nearest whole number.

Explanation:

To calculate the elevation of the mountain after 7 millennia considering it loses 1% of its elevation every millennium, we can apply the formula for exponential decay, which is P(t) = P0 imes (1 - r)^t, where P(t) is the future elevation, P0 is the initial elevation, r is the rate of erosion, and t is the number of time periods (in this case, millennia).

The initial elevation is 953 meters, and the rate of erosion is 1% or 0.01 when expressed as a decimal. Therefore, after 7 millennia, the height of the mountain will be:

P(7) = 953 times (1 - 0.01)^7

Calculating this gives us:

P(7) = 953 times 0.99^7 \\ P(7) = 953 times 0.9320653479069899 \\ P(7) \\\\ About 888 meters (rounded to the nearest whole number)

The mountain's height after 7 millennia would be approximately 888 meters.

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