The population of a certain city was 299000 in 1998, and the observed relative growth rate is 5 percent per year. (a) Find a function that models the population after t years. Your answer is (299000)(1.05)^t (b) Find the projected population in the year 2004. Your answer is 4672 (c) In what year will the population reach 774277? Your answer is 2017
The population of a certain city was 299000 in 1998, and the observed relative growth rate is 5 percent per year. (a) Find a function that models the population after t years. Your answer is (299000)(1.05)^t (b) Find the projected population in the year 2004. Your answer is 4672 (c) In what year will the population reach 774277? Your answer is 2017
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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How do I solve part b? I know that part a and c are correct but I'm having a hard time trying to figure out what number to plug into t for the exponent.
![**Population Growth Model**
The population of a certain city was 299,000 in 1998, and the observed relative growth rate is 5 percent per year.
**(a) Find a function that models the population after \( t \) years.**
The function provided is:
\[ P(t) = 299000 \times (1.05)^t \]
**(b) Find the projected population in the year 2004.**
The answer given is:
\[ P(2004) = 4672 \]
(Note: The calculation seems incorrect. The function should be applied as follows: \( P(2004) = 299000 \times (1.05)^6 \).)
**(c) In what year will the population reach 7,742,277?**
The year provided is:
\[ 2017 \]
These steps illustrate how exponential growth functions can be used to model population changes over time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e19c53d-6e05-4933-8b85-01b8c70e7dd1%2F6983a50c-14b1-41d9-a3af-07b7211219b1%2Fzp210ao_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Population Growth Model**
The population of a certain city was 299,000 in 1998, and the observed relative growth rate is 5 percent per year.
**(a) Find a function that models the population after \( t \) years.**
The function provided is:
\[ P(t) = 299000 \times (1.05)^t \]
**(b) Find the projected population in the year 2004.**
The answer given is:
\[ P(2004) = 4672 \]
(Note: The calculation seems incorrect. The function should be applied as follows: \( P(2004) = 299000 \times (1.05)^6 \).)
**(c) In what year will the population reach 7,742,277?**
The year provided is:
\[ 2017 \]
These steps illustrate how exponential growth functions can be used to model population changes over time.
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