Rats have recently become a nuisance in Norwood. Efforts to control the rat problem have led to the rat population declining by 15% every year. If the town currently has 13,000 rats, how many rats will there be in 3 years?If necessary, round your answer to the nearest whole number.
Question
Rats have recently become a nuisance in Norwood. Efforts to control the rat problem have led to the rat population declining by 15% every year. If the town currently has 13,000 rats, how many rats will there be in 3 years?If necessary, round your answer to the nearest whole number.
Solution
To solve this problem, we need to apply the formula for exponential decay, which is:
N = N0 * (1 - r)^t
where: N is the final amount (the number of rats after 3 years), N0 is the initial amount (the current number of rats, which is 13,000), r is the rate of decline (15%, or 0.15 when expressed as a decimal), and t is the time (3 years).
Substituting the given values into the formula, we get:
N = 13000 * (1 - 0.15)^3
First, calculate the value of (1 - 0.15), which is 0.85.
Then, raise 0.85 to the power of 3, which gives approximately 0.614.
Finally, multiply 13000 by 0.614, which gives approximately 7982.
So, there will be around 7982 rats in Norwood in 3 years, if the current rate of decline continues.
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