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 400,000 mosquitoes in the area initially, and predators (birds, bats, and so forth) eat 50,000 mosquitoes/day. determine the population of mosquitoes in the area at any time. (note that the variable t represents days.) enter an exact answer. enclose arguments of functions in parentheses. for example, sin(2x).

Population of mosquitoes in the area at any time t is:

Step-by-step explanation:

assume population at any time t = P(t)

population increases at a rate proportional to the current population:

⇒dP/dt ∝ P

 ----(1)

where k is constant rate at which population is doubled

solving (1)

---- (2)

initial population = 400,000

population is doubled every week

                                                 ⇒P(1)=2P(0)

Using (2)

In presence of predators amount is decreased by 50,000 per day

Then amount decreased per week = 350,000

In this case (1) becomes

---(3)

solving (3) by calculating integrating factor

Multiplying I.F with all terms of (3)

Integrating w.r.to t

at t=0

So, population of mosquitoes in the area at any time t is

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,