Question 4 of 11 , Step 1 of 1 $3 / 15$ Correct 2 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. Answer Keypa How to enter your answer (opens in new window) Keyboard Shortc people

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.