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
kondor19780726 [428]
2 years ago
11

The concentration of dichlorodiphenyltrichloroethane (DDT - an infamous pesticide) in Lake Michigan has been declining exponenti

ally over many years. In 1971, the DDT concentration was 13.00 ppm (parts per million). In 1984, the DDT concentration was 2.22 ppm.
Using these data points, determine the exponential decay function to model the DDT concentration decline in terms of years, tt, where t=0t=0 represents the year 1971.


A) Write your function as y = Ce^{rt}y=Ce^rt. Round your value of rr to four decimal places.


B) Another way to write the function down is known as the half-life formula, written as y = C(0.5)^{t/H}y=C(0.5)^t/H, where HH is the time required for the concentration to get cut in half. Using the initial two data points, find the value of HH, rounded to 2 decimal places. Show all Algebraic work.


C) The goal was to reduce the DDT concentration to 0.98 ppm by 1995. Was this possible according to your model?
Mathematics
1 answer:
mojhsa [17]2 years ago
8 0

Answer: A) y=13e^{-0.1359t}

              B) H = 5.10

              C) Yes

Step-by-step explanation: <u>Exponential</u> <u>Decay</u> <u>function</u> is a model that describes the reducing of an amount by a constant rate over time. Generally, it is written in the form: y(t)=Ce^{rt}

A) C is initial quantity, in this case, the initial concentration of DDT. To determine r, using the data given:

y(t)=Ce^{rt}

2.22=13e^{13r}

e^{13r}=0.1708

Using a natural logarithm property called <em>power rule:</em>

13r=ln(0.1708)

r=\frac{ln(0.1708)}{13}

r=-0.1359

The decay function for concentration of DDT through the years is y(t)=13e^{-0.1359t}

B) The value of H is calculated by y=C(0.5)^{\frac{t}{H} }

2.22=13(0.5)^{\frac{13}{H} }

(0.5)^{\frac{13}{H} }=0.1708

Again, using power rule for logarithm:

\frac{13}{H} log(0.5)=log(0.1708)

\frac{13}{H} =\frac{log(0.1708)}{log(0.5)}

\frac{13}{H} =2.55

H = 5.10

Constant H in the half-life formula is H=5.10

C) Using model y(t)=13e^{-0.1359t} to determine concentration of DDT in 1995:

y(24)=13e^{-0.1359.24}

y(24) = 0.5

By 1995, the concentration of DDT is 0.5 ppm, so using this model is possible to reduce such amount and more of DDT.

You might be interested in
HELP PLEASE!!!<br>What is the ratio of 1713.57^2/4113.87^3.
antiseptic1488 [7]

Answer:

  4.21747×10^-5

Step-by-step explanation:

Your calculator can do the division for you. The ratio is about 4.21747×10^-5.

__

This is approximately 10/237109.

6 0
2 years ago
A research team is testing whether a fuel aditive increases a car's gas mileage. The maker of the additive claims that the addit
Thepotemich [5.8K]

Answer:

Yes  there is sufficient evidence to  reject the company's evidence

Step-by-step explanation:

From the question we are told that  

   The sample size is  n =  25

    The mean is  \= x = 5.3 \ mpg

     The standard deviation is  \sigma = 1.8 \  mpg

    The z-score is  z = -1.94

The null hypothesis is  H_o : \mu = 6 \ mpg

The alternative hypothesis is  H_a :  \mu \ne 6

 Generally the p-value is mathematically evaluated as  

           p-value   =  2 * P( Z

From the z table  the area under the normal curve to the left corresponding to    -1.94  is

         P( Z

=>  p-value   =  2 * 0.02619

=>  p-value   =  0.052

Let assume the level of significance is  \alpha = 0.05

 Hence the  p-value > \alpha this mean that

   The  decision rule is  

Fail to reject the null hypothesis

The conclusion is

 There is sufficient evidence to  reject the company's evidence

 

5 0
3 years ago
Charlie is cleaning her closet. She
Soloha48 [4]

Answer:

9 shirts

Step-by-step explanation:

12 - 6 = 6

6/2 = 3

3 times 3 = 9

8 0
3 years ago
Creating a One-Variable Equation to Model and Solve a Problem
guajiro [1.7K]

Answer:

The hourly fee for rototiller is $3 per hour.

Step-by-step explanation:

We are given the following in the equation:

The rental company  charged an initial fee of $43 with an additional fee per hour.

Let h represents the hourly fee.

The family paid $64 after renting the rototiller for 7 hours.

Thus, we can write the equation:

43 + 7h = 64

Solving the equation, we get,

43 + 7h = 64\\7h = 64-43\\7h = 21\\\Rightarrow h = 3

Thus, the hourly fee is $3 per hour.

Equation:

C(x) = 43 + 3x

where C(x) is the cost function and x is the number of hours rototiller is rented.

The hourly fee for rototiller is $3 per hour.

4 0
3 years ago
Which property would allow you to use mental computation to simplify the problem 27 + 15 + 3 + 5? additive identity additive inv
Fofino [41]

Answer:

Commutative Property

Step-by-step explanation:

Additive Identity: If you add a real number to zero or add zero to a real number, then you get the same real number back.

Additive Inverse: When you add the same number but reversed sign, you get 0.

Commutative Property: a + b = b + a

Addition distributive property: a(b+ c) = ab + ac.

In this case, we use the commutative property:

27 + 15 + 3 + 5 = 27 + 3 + 15 + 5.

We know that 27 + 3 = 30 and 15 + 5 = 20, so we get 50 quickly using mental math.

5 0
3 years ago
Read 2 more answers
Other questions:
  • Each letter in the word "mathematics" is written on a slip of paper and placed in a box. Lynette chooses a letter from the box,
    10·2 answers
  • What is the value of (-7 + 3i) - (2-6i)?
    10·2 answers
  • Will Give BRAINLIEST for CORRECT answer! Please Help! A can of vegetables holds 454 mL of food and is 4.5 in. tall. What is the
    10·2 answers
  • Six pairs of socks cost as much as 1 coat, 2 pairs of jeans cost as much as 3 pairs of shoes, and 4 pairs of socks cost as much
    10·1 answer
  • Please help on this one
    9·2 answers
  • Determine whether the formula describes y as a function of x. Explain your reasoning. Y=9x+1
    10·1 answer
  • Pls help me with this
    9·1 answer
  • What is the length of the hypotenuse in a right triangle with legs of length 14 and 48?
    6·2 answers
  • The taxiFair in Gotham city is $2.40 for the first half mile additional mileage Charged at the rate of $.20 for each additional
    5·1 answer
  • Complete the equation for f(x)
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!