Question

The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate of $$4500 \sqrt{t}+1000$$ people/year, $t$ years from the start of construction. The population before construction is 30,000 . Determine the projected population 9 years after construction of the park has begun.

Name: Problem 76, Chapter 6: Applied Calculus for the MLSS A Brief Approach
Uploaded: 2021-08-01T00:00:00-08:00
Duration: 1 min 30 s
Channel: Lucas Finney
Description: The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate of 4500 √(t)+1000 people/year, t years from the start of construction. The population before construction is 30,000 . Determine the projected population 9 years after construction of the park has begun.

   The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate of $$4500 \sqrt{t}+1000$$
people/year, $t$ years from the start of construction. The population before construction is 30,000 . Determine the projected population 9 years after construction of the park has begun.

Applied Calculus for the MLSS A Brief Approach

Soo T. Tan 10th Edition

Chapter 6, Problem 76

Instant Answer

Solved by Expert Lucas Finney

08/01/2021

Step 1

We are also given that the initial population before construction is 30,000. Show more…

Show all steps

Thanks for your feedback!

The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate of $$4500 \sqrt{t}+1000$$ people/year, $t$ years from the start of construction. The population before construction is 30,000 . Determine the projected population 9 years after construction of the park has begun.

Play audio

Feedback

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Initial Value Problem

An initial value problem involves computing a function by integrating its rate of change while considering an initial condition. The initial population serves as the baseline value, and by adding the accumulated change (found through integration) to this baseline, we can predict the future population.

Definite Integration

Definite integration is used to calculate the total accumulation of a quantity by summing up a continuous rate of change over a specified interval. In growth models, it allows us to find the total increase in population over time by integrating the rate function between two time points.

Rate of Change

The rate of change represents the derivative of a quantity with respect to time, indicating how fast that quantity is increasing or decreasing. In population models, the rate function describes how the population grows every year, and understanding this function is key to estimating total growth.

Please give Ace some feedback