Question

A mountain in Lincoln County is eroding and losing elevation at a rate of 5% every millennium. If the current elevation is 1,283 meters, how tall will the mountain be in 2 millennia?round your answer to the nearest whole number.

Answer 1

EXPLANATION

We need to apply the exponencial decay in order to get the final elevation of the mountain:

$f(t)=a(1-r)^t$

Where a is the initial value, a=1,283 meters and r is the rate in decimal form r= 5/100 = 0.05 and t = time = 2 millenials

Then, we need to substitute the terms:

$f(t)=1,283\cdot(1-0.05)^2$

Subtracting numbers:

$f(t)=1,283\cdot0.95^2$

Computing the power:

$f(t)=1,283\cdot0.9025$

Multiplying numbers:

$f(t)=1157.90\text{ meters}$

Rounding to the nearest whole number:

Final Elevation = 1158 meters