The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of other factors, the population doubles each week. There are 600,000 mosquitoes in the area initially, and predators (birds, bats, and so forth) eat 40,000 mosquitoes day. Determine the population of mosquitoes in the area any time. (Note that the variable t represents days.) Enter an exact answer Enclose arguments of functions in parentheses For example, sin (2r).

The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of other factors, the population doubles each week. There are 600,000 mosquitoes in the area initially, and predators (birds, bats, and so forth) eat 40,000 mosquitoes day. Determine the population of mosquitoes in the area any time. (Note that the variable t represents days.) Enter an exact answer Enclose arguments of functions in parentheses For example, sin (2r).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

### Exponential Growth of Mosquito Population

**Description:**
The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of other factors, the population doubles each week. There are 600,000 mosquitoes in the area initially, and predators (birds, bats, and so forth) eat 40,000 mosquitoes per day. Determine the population of mosquitoes in the area at any time. (Note that the variable t represents days.)

**Instructions:**
Enter an exact answer.
Enclose arguments of functions in parentheses. For example, sin(2x).

**Equation to Determine Population:**

\[ P(t) = \]

**Input Field:**
\[
\boxed{\rule{3cm}{0.4pt}}
\]

Provide the initial conditions and related calculations based on the doubling rate and predation for accurate results.

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