answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ne4ueva [31]
1 year ago
12

One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number o

f sterile males that mate with fertile females but produce no offspring. let p represent the number of female insects in a population and s the number of sterile males introduced each generation. let r be the per capita rate of production of females by females, provided their chosen mate is not sterile. then the female population is related to time t by t = p + s p[(r − 1)p − s] dp. suppose an insect population with 10,000 females grows at a rate of r = 1.2 and 400 sterile males are added. evaluate the integral to give an equation relating the female population to time. (note that the resulting equation can't be solved explicitly for p. remember to use absolute values where appropriate.)
Mathematics
1 answer:
Zielflug [23.3K]1 year ago
8 0

To be clear, the given relation between time and female population is an integral:<span>
</span>t = \int { \frac{P+S}{P[(r - 1)P - S]} } \,&#10;dP<span>

</span>

<span>The problem says that r = 1.2 and S = 400, therefore substituting:<span>
</span>t = \int { \frac{P+400}{P[(1.2 - 1)P - 400]}&#10;} \, dP<span>

</span>= <span><span>&#10;\int { \frac{P+400}{P(0.2P - 400)} } \, dP

In order to evaluate this integral, we need to write this rational function in a simpler way:
</span>\frac{P+400}{P(0.2P - 400)} = \frac{A}{P} +&#10;\frac{B}{(0.2P - 400)}</span><span>

</span>where we need to evaluate A and B. In order to do so, let's calculate the LCD:<span>
</span>\frac{P+400}{P(0.2P - 400)} = \frac{A(0.2P -&#10;400)}{P(0.2P - 400)} + \frac{BP}{P(0.2P - 400)}<span>

</span>the denominators cancel out and we get:<span>
</span>P + 400 = 0.2AP - 400A + BP<span>
</span>             = P(0.2A + B) - 400A<span>

</span>The two sides must be equal to each other, bringing the system:<span>
</span>\left \{ {{0.2A + B = 1} \atop {-400A =&#10;400}} \right.<span>

</span>Which can be easily solved:<span>
</span>\left \{ {{B=1.2} \atop {A=-1}} \right.<span>

</span>Therefore, our integral can be written as:<span>
</span>t = \int { \frac{P+400}{P(0.2P - 400)} } \,&#10;dP = \int {( \frac{-1}{P} + \frac{1.2}{0.2P-400} )} \, dP<span>
</span>= - \int { \frac{1}{P} \, dP +&#10;1.2\int { \frac{1}{0.2P-400} } \, dP<span>
</span>= - \int { \frac{1}{P} \, dP +&#10;6\int { \frac{0.2}{0.2P-400} } \, dP<span>
</span>= - ln |P| + 6 ln |0.2P - 400| + C<span>

</span>Now, let’s evaluate C by considering that at t = 0 P = 10000:<span>
</span>0 = - ln |10000| + 6 ln |0.2(10000) - <span>400| + C
C = ln |10000</span>| - 6 ln |1600|<span>
</span>C = ln (10⁴) - 6 ln (2⁶·5²)<span>
</span>C = 4 ln (10) - 36 ln (2) - 12 ln (5) <span><span>
</span></span><span><span> </span>Therefore, the equation relating female population with time requested is:<span>
</span><span>t =  - ln |P| + 6 ln |0.2P - 400| + 4 ln (10) - 36 ln </span>(2) - 12 ln (5)</span></span>
You might be interested in
6. Problems and Applications Q6 Consider an economy that produces only chocolate bars. In year 1, the quantity produced is 3 bar
natulia [17]

Answer:

Year 1 GDP Deflator is 100%

Year 2 GDP Deflator is 30%

Year 3 GDP Deflator is 14.29%

Inflation Rate between year 2 and year 3 is 50%

The Real GDP growth Rate for Year 2 and year 3 is 110%

Step-by-step explanation:

Year 1  

 Price of chocolate bar is $2 and 3 bars are sold that year so the real GDP is 3 x $2=$6 which we are also given that this year is the nominal base year so the nominal GDP is also $6. GDP is the sum of all market value produced products in an economy. Therefore that’s why we calculated as the price of a chocolate multiplied the number produced. To calculate the GDP Deflator will be as follows:

GDP Deflator= (nominal GDP/Real GDP) x 100

                      = ($6/$6) x 100

                       = 100%  

Year 2

Price of chocolate bars is $4 per bar and 5 bars were produced therefore Real GDP =$4 x 5 = $20, now we will calculate the GDP deflator as we have been told that year  is the nominal year therefore nominal GDP is $6.

GDP Deflator= (nominal GDP/Real GDP) x 100

                       = ($6/$20) x100

                        = 30%

Year 3

Price of chocolate bars is $6 per bar and 7 bars were produced therefore Real GDP =$6 x 7 =$42, now we calculate the GDP deflator as we have been told that year 1 is the nominal year therefore nominal GDP is $6.

GDP Deflator = (nominal GDP/ Real GDP) x 100

                      = ($6/$42)

                       =14.29%

Now we calculate the inflation rate between year 2 and year 3.we use the CPI (consumer price index to get the inflation rate for year 2 ad 3)

Consumer Price Index = (Current price of bar/previous price of bar) x 100 formula for CPI

                      = ($6/$4) x 100= 150%-100%

                         = 50% is the inflation rate as the consumer price gave us a positive value.

Now we compute the real GDP growth rate between year 2 and year 3

Real GDP growth rate = [  (current Real GDP- Previous Real GDP)/Previous Real GDP] x 100

                                      = ($42-$20)/$20

                                       = 110% so real GDP grew by 110% from year 2 to year 3.

8 0
2 years ago
Wynn needs to find the center of the data set shown on the dot plot. The dot plot has dots. The dot plot has dots to the left of
Arisa [49]

Answer:

The dot plot has  22

dots.

The dot plot has   11

dots to the left of the

center and   11

dots to the right of the center.

The center of the data set is  

between 2 and 3

.

Step-by-step explanation:

6 0
1 year ago
WILL GIVE BRAINLIEST ANSWER!!
Natasha2012 [34]
Check the picture below.

now, bear in mind that, there are 60minutes in 1 degree, so 23' is just 23/60 degrees or about 0.38 degrees.

and 29' is just 29/60 degrees or about 0.48 degrees.

so 16°23' is about 16.38°, and 49°29' is about 49.48°

\bf tan(16.38^o)=\cfrac{200}{a+b}\implies a+b=\cfrac{200}{tan(16.38^o)}&#10;\\\\\\&#10;\boxed{b=\cfrac{200}{tan(16.38^o)}-a}&#10;\\\\\\&#10;tan(49.48^o)=\cfrac{200}{b}\implies \boxed{b=\cfrac{200}{tan(49.48^o)}}\\\\&#10;-------------------------------\\\\&#10;\cfrac{200}{tan(49.48^o)}=\cfrac{200}{tan(16.38^o)}-a\\\\\\a=\cfrac{200}{tan(16.38^o)}-\cfrac{200}{tan(49.48^o)}

make sure your calculator is in Degree mode.

4 0
2 years ago
Read 2 more answers
Athletes in a particular sport are classified as either offense or defense. The distribution of weights for the athletes classif
Evgen [1.6K]

Answer:

E. Bimodal.

Step-by-step explanation:

6 0
1 year ago
Is the average (arithmetic mean) of x and y greater than 20? the average (arithmetic mean) of 2x and 2y is 48. x = 3y?
AysviL [449]
2x + 2y = 48
2(x + y) = 48
x + y = 24
mean = 24/2 = 12

less than 20
4 0
2 years ago
Other questions:
  • The surface areas of two similar solids are 312 ft2 and 1,198 ft2. The volume of the smaller solid is 239 ft3. What is the volum
    13·2 answers
  • Suppose that a is a square matrix with characteristic polynomial (λ − 3)2(λ − 6)3(λ + 1). (a) what are the dimensions of a? (giv
    14·1 answer
  • To raise money to attend Boy Scout camp Alec is selling popcorn.?small bags of popcorn sell for $4 each and large bag sale for $
    8·2 answers
  • Solve the following multiplication and division problems. a. 8 T. 1,398 lb. 14 oz. × 6 b. 349 lb. 6 oz. ÷ 130 c. 6 T. 294 lb. ÷
    11·2 answers
  • Alissa is analyzing an exponential growth function that has been reflected across the y-axis. She states that the domain of the
    9·2 answers
  • A jet plane travels 2 times the speed of a commercial airplane. The distance between Vancouver
    15·1 answer
  • Egbert is making trail mix out of 18 bags of nuts and 9 bags of dried fruit. He wants each new portion of trail mixto be identic
    13·1 answer
  • For three minutes the temperature of a feverish person has had negative first derivative and positive second derivative.
    7·1 answer
  • A consumer protection agency is testing a sample of cans of tomato soup from a company. If they find evidence that the average l
    13·1 answer
  • Emerson purchased a game that was on sale for 18% off. The sales tax in his county is 8%. Let y represent the original price of
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!