a mountain in boone county is eroding and losing elevation at a rate of 5% every millennium. if the current…

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. Here, ( P = 1710 ) meters, ( r = 0.05 ) (since 5% = 0.05), and ( t = 4 ) millennia.

Step2: Substitute the values into the formula

Substitute ( P = 1710 ), ( r = 0.05 ), and ( t = 4 ) into the formula: ( A = 1710(1 - 0.05)^4 ) First, calculate ( 1 - 0.05 = 0.95 ).

Step3: Calculate ( 0.95^4 )

( 0.95^4 = 0.95 \times 0.95 \times 0.95 \times 0.95 ) ( 0.95 \times 0.95 = 0.9025 ) ( 0.9025 \times 0.95 = 0.857375 ) ( 0.857375 \times 0.95 \approx 0.81450625 )

Step4: Multiply by the initial amount

( A = 1710 \times 0.81450625 ) ( 1710 \times 0.81450625 = 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