A sample of bacteria is decaying according to a half-life model. If the sample begins with 800 bacteria, and after 14 minutes there are 160 bacteria, after how many minutes will there be 40 bacteria remaining? Round your answer to the nearest whole number.

Q: Suppose a sample of a certain substance decayed to 73.2% of its original amount after 300 days.…

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Q: In the early 1960s, radioactive strontium-90 was released during atmospheric testing of nuclear…

A: the radioactive decay is a continuous process. Therefore, A=A0ert where A is the amount remaining,…

Q: Element X decays radioactively with a half life of 11 minutes. If there are 300 grams of Element X,…

A: Given information: The half life h =11 min, there are 300g of element X. To find: The time it will…

Q: If the population of a small city is 45,000. If the population grows continuously by 5% per​ year,…

A: Here we use compound interest based formula. If p is present population, r is rate of growth of…

Q: If 250 mg of a radioactive element decays to 200 mg in 53 hours, find the half-life of the element…

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Q: Suppose you have a cache of radium, which has a half-life of approximately 1590 years. How long…

A: Given: Half-life of radium = 1590 years To find: Time taken to disappear 1/4 of the radium. Formula…

Q: WThe half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows…

A: Given : The half life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a…

Q: * Find the decay rate of each scenario below. 1. If the half-life is 6, what is the decay rate? 2.…

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Q: In the early 1960s, radioactive strontium-90 was released during atmospheric testing of nuclear…

A:

Q: In the 2000 U.S. Census, a small city had a population of 45,000. By 2010, the population had…

A: The population is increasing per year at a constant percentage of its population. to find the year…

Q: The half-life of strontium-90 is 28 years. How long will it take a 40 mg sample to decay to a mass…

A:

Q: Suppose you have a cache of radium, which has a half-life of approximately 1590 years. How long…

A: Given that Half life of radium is 1590 years To find How long would you have to wait for 1/8 of it…

Q: If half a certain amount of radium decays in 1600 years. What percentage of the original amount will…

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Q: In the 2000 U.S. Census, a small city had a population of 40,000. By 2010, the population had…

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Q: If the population of Austin was 0.8 million in 2018 and has been growing at 1.80% continuously. When…

A: For the solution follow the next step.

Q: Lead-210 has a half-life of 22.3 years. How much of a 102-mg sample would be remaining after 6 years

A: To solve such problem we use the following two equations K=0.693t12 N=N0e−Kt Given that T12=22.3…

Q: If 250mg of a radioactive element decays to 190mg in 12 hours, find the half-life of the…

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Q: The population of a southern city follows the exponential law. If the population doubled in size…

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Q: A sample of radium has a weight of 1.5 mg and a half life of approximately 6 years. How much of the…

A: Given Data: The weight of the sample of radium is: W=1.5 mg The approximate half-life of the sample…

Q: If the population of a certain city was 100,000 in 1996 and 110,643 in 2006, and if the population…

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Q: A sample of bacteria is decaying according to a half - life model . If the sample begins with 500…

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Q: A scientist wants to determine the halflife of a certain radioactive substance. She determines that…

A: The half life function is given by: N(t)=N0(0.5)t/t1/2 where N(t) is the final amount in milligrams…

Q: In the 2000 U.S. Census, a small city had a population of 45,000. By 2010, the population had…

A: Given  Population in 2000 = 45,000  Population in 2010 = 65148

Q: suppose a sample of a certain substance decayed to 77.2% of its original amount after 300 days. (two…

A: Let t        = time in daysN(t)  =remaining quantity of certain substance at any time 't'No…

Q: A new car is purchased for $33,000 and over time its value depreciates by one half every 4 years.…

A: Ao=Initial value of the car At= Value of the car after "t" years Given: Cost of the new car…

Q: The half life of a decaying substance is the amount of time it takes for the substance to reduced to…

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Q: A sample of bacteria is decaying according to a half-life model. If the sample begins with 500…

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Q: If 16% of a radioactive substance decays in 13 hours, what is the half-life of the substance? Round…

A: In case of a radioactive decay,  the amount x after time t is given by x(t)=x(0)e−kt where x(0) is…

Q: a car sells for $12,500 and one year later it is valued at $11,375. find the decay rate of the car

A: Explanation of the answer is as follows

Q: The half-life of strontium-90 is 28 years. How long will it take a 44 mg sample to decay to a mass…

A: We can solve this as follows:

Q: In the 2000 U.S. Census, a small city had a population of 50,000. By 2010, the population had…

A:

Q: An article on the "Iceman" stated that the frozen corpse was 5,000 to 5,500 years old. Assuming the…

A: Given data: The given time is t=5,200 years. The given half lifetime is t1/2=5,730. The expression…

Q: The growth rate of a certain strain of bacteria is unknown, but assumed to be constant. When an…

A: Given that the bacteria is growing at a constant rate. Initially there were 1500 bacteria and after…

Q: Use the exponential decay model, A = A0ekt, to solve:The half-life of thorium-229 is 7340 years. How…

A: Given exponential decay function: A=A0ekt......(1) where A0, of radioactive substance, A represents…

Q: The size of a threatened population of bottlenosed dolphins is decaying exponentially with a…

A: we have to slove the above question

Q: If the population of a small city is 55,000. If the population grows continuously by 5​% per​ year,…

A:

Q: The​ half-life of a radioactive substance is 25 years. If you start with some amount of this​…

A: Given: Half life of a radioactive substance is 25 years. Concept used: Here we shall use the formula…

Q: Use the exponential decay model, A = A0ekt, to solve. Round answers to one decimal place. The…

A: Given  we have to use  A = A0ekt The half life of thorium is 7340 years

Q: For a certain patient, a dose of Acetaminophen decays exponentially in their blood stream with a…

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Q: how long ago was the map drawn​ up? Round to the nearest year. Does the age of the map support its​…

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Q: The half-life of strontium-90 is 28 years. How long will it take a 60 mg sample to decay to a mass…

A: This can be solved using the following way....

Q: If 250 mg of a radioactive element decays to 220 mg in 12 hours, find the half-life of the element.…

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Q: Suppose you have a cache of radium, which has a half-life of approximately 1590 years. How long…

A: Given, you have a cache of radium, which has a half-life of approximately 1590 years.

Q: The half life of a radioactive isotope is 70 years. If 150 grams of the isotope is originally…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: A sample of bacteria is decaying according to a half-life model. If the sample begins with 500…

A: The decay function is: P(t)=P0ekt Given P0=500. So, P(t)=500ekt Now given that P(14)=100. So, the…

Q: a) If an investment grows in value at 2.4% per year, how long will it take for its value to double?…

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Q: The radioactive isotope gallium 67 has a biological half-life of 36 hours. If we start with 100…

A: The half life of the radioactive element is the time during which half of the radioactive element…

Q: Element X decays radioactively with a half life of 12 minutes. If there are 690 grams of Element X,…

A:

Q: A wooden statue found in Egypt has a carbon-14 content that is three-fifths of that found in living…

A: The given problem is solved below in detail.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.