Question

A certain first covers an area of 4100 km^2. Each year this area decreases by 3.75 percent. What will the area be after 11 years?

Answer 1

The formula to use is

A = P(1+r)^t

where,

A = final amount after t years

P = initial amount = 4100

r = rate of increase or decay = -3.75% = -3.75/100 = -0.0375

t = number of years = 11

The value of r is negative to indicate exponential decay. Also notice that I divided by 100 to convert from -3.75% to -0.0375

Using those values, we plug them into the formula to get,

A = P(1+r)^t

A = 4100(1+(-0.0375))^11

A = 4100(1-0.0375)^11

A = 4100(0.9625)^11

A = 4100*0.65676215615721

A = 2692.72484024457

A = 2693

Rounding to the nearest whole number, the answer is approximately 2693 km^2.