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The population of a certain inner-city area is estimated to be declining according to the model $\mathrm{P}(\mathrm{t})=201,000 \mathrm{e}^{-0.014 \mathrm{t}}$, where $t$ is the number of years from the present What does this model predict the population will be in 14 years? Round to the nearest person.
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\(\boxed{165224}\) is the predicted population in 14 years.
Step 1 ：Given the exponential decay model for population is \(P(t) = 201000 \cdot e^{-0.014t}\), where \(P(t)\) is the population at time \(t\), \(201000\) is the initial population, \(e\) is the base of the natural logarithm (approximately \(2.71828\)), \(-0.014\) is the decay rate, and \(t\) is the time in years.
Step 2 ：To find the population in 14 years, we substitute \(t = 14\) into the model.
Step 3 ：Calculating the result gives \(P = 201000 \cdot e^{-0.014 \cdot 14}\).
Step 4 ：Solving this gives \(P = 165224\).
Step 5 ：\(\boxed{165224}\) is the predicted population in 14 years.
