1answer.
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
xeze [42]
3 years ago
10

Scientists are monitoring the populations of two insect species in a remote location in Alabama. They estimate that the current

population of insect A is 2.5 million. But it’s declining at the rate of 4% per year because of habitat loss. The estimated population of insect B is 1.2 million, and it’s increasing at the rate of 200,000 per year. Let x represent the population of each insect species in millions, and y represent the elapsed time in years. Which equation can be used to determine how long it will take for the populations of the two species to be equal? 2.5e-0.04x = 1.2 + e0.2x 2.5e0.04x = 1.2 + 0.2x 2.5e-0.04x = 1.2 + 0.2x 2.5 + 0.04x = 1.2 + 0.2x
Mathematics
1 answer:
bulgar [2K]3 years ago
3 0

Answer:

2.5e-0.04x = 1.2 + 0.2x

Step-by-step explanation:

Given that:

Insect A:

Initial population, Po = 2.5 million

Rate of decline = 4%

Insect B:

Initial Population (Po) = 1.2 million

Yearly increase = 200,000 = (200,000/1,000,000) = 0.2

For insect A:

P(t) = Po(1 - r)^t = Po*e^-rt

Po*e^-rt = 2.5e^-0.04t ----(1)

For Insect B:

P(t) = Po + (yearly increase) * t

P(t) = 1.2 + 0.2t - - - - - (2)

Equating (1) and (2)

2.5e^-0.04t = 1.2 + 0.2t

You might be interested in
What is the rate of change
kow [346]
The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.
3 0
2 years ago
Read 2 more answers
What percent of 500 is 50?​
mestny [16]

Answer:50/500×100=10%

Therefore, 10% of 500 is 50.

Hope this answer helps you...

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Bertie Bee's Carpet Cleaners charge $1.22 per square foot to clean carpets. Millie Mott's Carpet Cleaners charge $9.50 per squar
Crank

Answer:

Bertie Bee's Carpet Cleaners

6 0
2 years ago
Which overlapping triangles are congruent by ASA?
Elena-2011 [213]

Answer:

D. ADC EBC

Step-by-step explanation:

cb & cd have that little line showing they're the same

5 0
3 years ago
Read 2 more answers
Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research
kolbaska11 [484]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

Yes the researcher can  conclude that the supplement has a significant effect on cognitive skill

b

d =  0.5778

c

The result of this hypothesis test shows that there is sufficient evidence to  that the supplement had significant effect.The measure of effect size is  large due to the large value of Cohen's d (0.5778 > 0.30 )

Step-by-step explanation:

From the question we are told that

  The sample size is  n=16

    The sample mean is  M  =  50.2

    The standard deviation is \sigma  = 9

    The  population mean is  \mu =  45

     The level of significance is  \alpha =  0.05

The null hypothesis is H_o  \mu =45

The alternative hypothesis is H_a  \mu \ne 45

Generally the test statistics is mathematically represented as

          z =  \frac{M -  \mu}{\frac{\sigma}{\sqrt{n} } }

=>       z =  \frac{50.2 - 45}{\frac{9}{\sqrt{16} } }

=>       z =  2.31

Generally the p-value is mathematically represented as

     p-value  =  2 *  P(Z >  z )

      p-value  =  2 *  P(Z >  2.31 )

From the z-table  

      P(Z >  2.31 ) = 0.010444

=>     p-value  =  2 *  0.010444

=>     p-value  =  0.021

From the obtained values we see that p-value <  0.05

 Decision Rule

 Reject the null hypothesis

Conclusion

There is sufficient evidence to conclude that the supplement has a significant effect on the cognitive skill of elderly adults

Generally the Cohen's d for this study is mathematically represented as

    d =  \frac{M  -  \mu}{\sigma }

=>  d =  \frac{50.2 -45}{9 }

=>  d =  0.5778

3 0
3 years ago
Other questions:
  • Is y = 4/x + 3 a linear equation?<br> is y = -2x - 4 a linear equation?
    6·1 answer
  • Find a particular solution to<br> y′′+6y′+5y=18te^(2t).
    10·1 answer
  • What are the solution(s) to the quadratic equation x2 – 25 = 0?
    13·2 answers
  • I am once again asking for your mathematical support​
    5·1 answer
  • I NEED HELP WITH 2 QUESTIONSS
    14·1 answer
  • The measures of Zx and Zy are equal. Which is the value of m?<br> 3(m + 2)<br> 5m - 58
    5·1 answer
  • No or yes <br> I need help
    7·1 answer
  • If p=20 and q=5, evaluate the following expression:3p−2q/5​
    14·2 answers
  • What is the slope of the line?
    15·1 answer
  • If cx - d = f, then x is equal to
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!