Answer:
a. To find the factor by which the area decreases in 10 years, we can use the formula for exponential decay: A(t) = A0 * e^(-kt) where A0 is the initial area, k is the decay constant, and t is the time in years.
Given that A(t) = 11 -0.98^t.
so, we can say k =0.98
The area after 10 years will be:
A(10) = 11 - 0.98^10
The decrease factor is:
(A(10)/A(0)) = (11 - 0.98^10)/11
b. To find the factor by which the area decreases each month, we can first convert the annual decay rate to a monthly rate by dividing by 12, since there are 12 months in a year.
So, the monthly decay rate is 0.98/12 = 0.0816
Then we can use the formula for exponential decay again with the new decay rate:
A(t) = A0 * e^(-kt)
The area after 1 month will be:
A(1/12) = 11 - 0.0816^(1/12)
The decrease factor is :
(A(1/12)/A(0)) = (11 - 0.0816^(1/12))/11
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