Question

the area covered by a lake is 11 square kilometers. It is decreasing exponentially at a rate of 2 percent each year represented by A(t)=11x(.98)^t. By what factor does the area decrease in 10 years? By what factor does the area decrease each month?

Answer 1

The lake decreases by a factor of 3.038 in 10 years (to 3.038 km^2).

The lake decreases by a factor of 0.00167 each month.

Explanation:

Use the given relationship A(t)=11x(.98)^t and find the value of A for t=10 years.

A(10) = 11*(0.98)^10

A(10) = 3.621 km^2

The lake has decreased by a factor of (11km^2/3.621km^2) or 3.038.

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The lake decreases each month by (0.02/12) or 0.00167 each month.