Problem
- Save \& Exit Certify Lesson: 7.2 Exponential Models SYDNEY GERBER Question 9 of 11, Step 1 of 1 8/13 Correct 1 The population of a certain inner-city area is estimated to be declining according to the model $P(t)=210,000 e^{-0.015 t}$, where $t$ is the number of years from the present. What does this model predict the population will be in 3 years? Round to the nearest person. Answer How to enter your answer (opens in new window) Keypad Keyboard Shortcut people
Solution
Step 1 ：The population of a certain inner-city area is estimated to be declining according to the model \(P(t)=210,000 e^{-0.015 t}\), where \(t\) is the number of years from the present. We are asked to predict the population in 3 years.
Step 2 ：We substitute \(t=3\) into the model. This gives us \(P(3)=210,000 e^{-0.015 \times 3}\).
Step 3 ：We calculate the value of \(P(3)\) to find the predicted population in 3 years. This gives us a population of approximately 200759.
Step 4 ：Since we are asked to round to the nearest person, the final predicted population in 3 years is \(\boxed{200759}\).
