Question

a mountain in boone county is eroding and losing elevation at a rate of 5% every millennium. if the current elevation is 1,710 meters, how tall will the mountain be in 4 millennia? if necessary, round your answer to the nearest whole number. meters submit

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay (as a decimal), and $t$ is the time.

Step2: Convert the rate to a decimal

The rate of erosion is 5% per millennium, so $r = 0.05$.

Step3: Identify the initial amount and time

The initial elevation $P = 1710$ meters, and the time $t = 4$ millennia.

Step4: Plug the values into the formula

$A = 1710(1 - 0.05)^4$
First, calculate $(1 - 0.05) = 0.95$. Then, $0.95^4 \approx 0.81450625$.
Now, multiply by the initial amount: $A = 1710 \times 0.81450625 \approx 1392.8056875$.

Step5: Round to the nearest whole number

Rounding $1392.8056875$ to the nearest whole number gives 1393.

Answer:

1393