The mass of a radioactive substance follows a continuous exponential decay model with a decay rate parameter of 7% per day. A sample of this radioactive substance was taken two days ago. If the sample has a mass of 3 kg today, find the initial mass of the sample. Round your answer to two decimal places.

Answers

Answer 1

The initial mass of the sample is approximately 3.45 kg.

To find the initial mass of the radioactive sample, we can use the exponential decay model. The general form of the exponential decay model is given by:

M(t) = M0 * [tex]e^{(-kt)}[/tex]

Where:

M(t) is the mass at time t,

M0 is the initial mass,

k is the decay rate parameter,

e is the base of the natural logarithm (approximately 2.71828).

In this case, we are given that the decay rate parameter is 7% per day, which can be written as k = 0.07. We also know that the mass of the sample today is 3 kg, and it was taken two days ago. Therefore, t = 2.

Using the given values in the exponential decay model equation, we can solve for the initial mass M0:

3 = M0 * [tex]e^{(-0.07 * 2)}[/tex]

Simplifying the equation:

3 = M0 * [tex]e^{(-0.14)}[/tex]

Dividing both sides by [tex]e^{(-0.14)}[/tex]:

[tex]M0 = 3 / e^{(-0.14)}[/tex]

Using a calculator, we can evaluate the right-hand side of the equation:

M0 ≈ 3 / 0.868745

M0 ≈ 3.45

Therefore, the initial mass of the sample is approximately 3.45 kg.

To learn more about initial mass from the given link

https://brainly.com/question/14410139

#SPJ4

Related Questions

When you trim a video, the ________ of the timeline indicates the portion of the video that will play during the slide; the ________ portion indicates the portion that is trimmed.

Answers

When you trim a video, the start and end markers of the timeline indicate the portion of the video that will play during the slide; the trimmed portion indicates the portion that is removed or excluded from the final playback.

When editing a video, you may want to remove certain parts or shorten its duration. Trimming allows you to specify the exact portion of the video that will be included in the final version. The timeline represents the entire duration of the video, and the start and end markers on the timeline serve as reference points for indicating the selected segment. By adjusting the position of these markers, you can define the beginning and end points of the desired portion. The section of the timeline between the start and end markers represents the portion of the video that will play during the slide or be included in the final output. The remaining parts of the video outside of this selected segment are considered the trimmed portion, which will be excluded from the playback or final edited version of the video.

Learn more about trim here:

https://brainly.com/question/31944873

#SPJ11

This place is being reformed by the Chinese government, since it became part of mainland China in 1999. What is this spot famous for

Answers

The spot referred to in the statement is Macau, which became part of mainland China in 1999. Macau is famous for being a former Portuguese colony and a major center for tourism and gambling in Asia.

Macau, known as the "Las Vegas of Asia," has a reputation for its vibrant and bustling casino industry. It attracts millions of tourists from around the world who visit to try their luck at the numerous casinos and experience the lively entertainment and nightlife. The city's skyline is adorned with iconic casino resorts and luxury hotels, contributing to its reputation as a premier destination for entertainment and leisure. Apart from its gambling scene, Macau also holds historical and cultural significance. The city's unique blend of Chinese and Portuguese influences is evident in its architecture, cuisine, and traditions. Macau's historic center, with its well-preserved colonial buildings and landmarks, has been designated as a UNESCO World Heritage site, attracting visitors interested in exploring the city's rich cultural heritage. The Chinese government's reforms since Macau's integration into mainland China have aimed to diversify its economy, enhance its tourism sector, and promote sustainable development. These efforts have included initiatives to strengthen cultural preservation, improve infrastructure, and expand the range of attractions beyond just gambling, making Macau a more well-rounded and appealing destination for visitors.

Learn more about gambling here:

https://brainly.com/question/10669380

#SPJ11

Other Questions

what was the first harvest like after the rebellion? who didn't do any of the hard work and why? The economy produces at a point______. where the isovalue line is tangent to the production possibility frontier. which is on the lowest possible the isovalue line. where the production possibility frontier intersects with one of the axes. which is on the highest isovalue line outside the production possibility frontier. which best describes the relationship between the force acting on an object the object's mass, and the acceleration of the object? a. newton's first law of motion b. newton's law of inertia c. newton's second law of motion d. newton's third law of motion a toddler is brought to the emergency department in cardiac arrest. the physician tries three times to insert an i.v. catheter but is unsuccessful. by which alternate route can the physician administer emergency medications? The accommodation limits for a nearsighted person's eyes are 20.0 cm and 60.0 cm. That is, this person's unaided eye has a near point of 20.0 cm and a far point of 60.0 cm. When this person wears his glasses, he can see faraway objects clearly. What is the closest distance at which he can see objects clearly when wearing his glasses the past five monthly returns for pg company are 1.25 percent, -1.50 percent, 4.25 percent, 3.75 percent, and 1.98 percent. what is the average monthly return? A catalyst facilitates a reaction by 1. lowering the activation energy of the reaction. 2. shifting the position of the equilibrium of the reaction. 3. decreasing the temperature at which the reaction will proceed spontaneously. 4. increasing the activation energy for the reverse reaction. 5. making the reaction more exothermic. all of these are examples of the importance of hormones for nutrition except ________. What is the minimum selling price on the special order to produce net income of 5.17 per basketball TRUE/FALSE which of the following is not true about gregorian chant (plainchant) melodies? contagion effects often work through the influence of a leader with a lot of: true/false. many brand managers and their agencies have increased the role of tv in their marcom budgeting because tv advertising is more cost-efficient than digital advertising the idea that black people in this country live in poverty is ridiculous. look at lebron james. he's a millionaire. and so are sean combs, samuel l. jackson, and michael jordan. a. False Cause. b. Weak Analogy. c. Hasty Generalization. d. Accident. Sheldon has been extremely afraid of cats since he was scratched as a 5-year-old. Whenever he sees a cat, he remembers the time he was scratched across his face, and he starts to feel afraid. If a cat comes toward him, he often runs away immediately, as he is afraid of being scratched again. Sheldon's behaviors and recollection of this trauma are a result of the __________ in the limbic system. The nurse assesses the bp in both arms of a newly admitted patient. Why would the nurse do this?. To forestall economic difficulties, which could foster the rise of communism throughout europe, the united states gave nearly $13 billion to a european recovery program called the. Redacta un pequeo texto donde expreses tu opinin de por qu a los jvenes no les gusta leer? what can a project manager do to avoid some of the pitfalls of a highly cohesive project team? (you may select more than one answer. single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer. any boxes left with a question mark will be automatically graded as incorrect.) check all that apply discourage functional conflict.unanswered personally show that one is a part of the team, and not so much a part of the organization.unanswered be proactive in reducing isolation.unanswered be aware that a highly cohesive team may lead to problems. what amount should company x reort on its balance sheet at year end if the investment in company k is considered a trading security and what amount shoud be reported if the ivnestment is considered an available for sale security Alex is resisting implementing automation in his area, not because he thinks it will harm the company but because he does not have experience with computers. This form of resistance to change would be classified as _________