Question

The area covered by a marsh, A, starts at 11500 acres and drops by a 1/4 each year for n years. Write a formula for A(n).

Answer 1

The formula for  that represent the area covered by a marsh A(n) is $A(n)=11500(\frac{1}{4} )^n$.

An exponential decay is given by the function:

y = abˣ

Where a is the initial value of y, b is a constant which is less than 1, y, x are variables.

Since the area covered by a marsh, A, starts at 11500 acres, hence a = 11500. Since the area drops by 1/4 each year for n years, hence:

$A(n)=11500(\frac{1}{4} )^n$

Therefore the formula for A(n) is $A(n)=11500(\frac{1}{4} )^n$

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