Please solve & show steps... **Problem: Mosquito Population Dynamics**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 initially 900,000 mosquitoes in the area, and predators (birds, bats, and so forth) consume 70,000 mosquitoes per day. Determine the population of mosquitoes in the area at any time \( t \), measured in days.**NOTE:** Enter an exact answer.**Equation to Determine the Population:**\[ P(t) = \]To solve this problem, consider the following steps:1. Understand how exponential growth works for the mosquito population.2. Integrate the predation rate into the model.3. Formulate the resulting differential equation.4. Solve the differential equation to find \( P(t) \), the population of mosquitoes at any time \( t \).Use your knowledge of differential equations, particularly those involving exponential growth and decay, to find an exact solution.

Name: Please solve & show steps... **Problem: Mosquito Population Dynamics**
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Please solve & show steps... **Problem: Mosquito Population Dynamics**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. Th