The decay of radioactive elements can sometimes be used to date events from Earth’s past. In a living organism, the ratio of radioactive carbon, carbon-14, to ordinary carbon stays fairly constant during the lifetime of the organism, being approximately equal to the ratio in the organism’s atmosphere at the time. After the organism’s death, however, no new carbon is ingested, and the proportion of carbon-14 in the organism’s remains decreases as the carbon-14 decays. Scientists who do carbon-14 dating often use a figure of 5730 years for its half-life. Find the age of a sample in which 10% of the radioactive nuclei originally present have decayed.

Q: If a population is recorded at 1,200 in the year 2000 and the rate of increase is a steady 50 people…

A: Given date  Initial population Po=1200 in the year 2000 (t=0) Rate of increase is a steady =50…

Q: The half-life of Carbon-13 is 5750 years. Samples taken at an excavation site show that a one…

A:

Q: A wooden artifact from an ancient tomb contains 20 percent of the carbon-14 that is present in…

A:

Q: Scientists can determine the age of ancient objects by the method of radiocarbon dating. The…

A: The half-life of the isotope is 5730 yrs.To Find:Estimate the age of the parchment.

Q: If the population of a country triple in 77 years, in how many years will it four times under the…

A: Need to find in how many years population will be 4 times

Q: The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the…

A: The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the…

Q: There are 5,000 wolves in the park, but their population is expected to decay at a rate of 8% per…

A: Given, initially , wolves in the park = 5000 Decay of population = 8% per year finally , wolves in…

Q: A news article states that the number of people infected with a particular virus has grown by 20% in…

A:

Q: An initial population of 8,000 decays for two years until the population is 500. By what percentage…

A: Given-  An initial population of 8,000 decays for two years until the population is 500. To…

Q: Suppose you possess some of a radioactive substance that has a half-life of 16 days. What fraction…

A: The half-life of a radioactive substance is the time it takes for half of the substance to decay. In…

Q: called diatoms, is a measure of the abundance of life in the lake. A rather complex variable based…

A: The regression is a method of machine learning under subgroup Supervised Learning. The regression…

Q: A radioactive substance has a half life of 175 years. Find the decay constant, r, for this…

A: A radioactive substance has a half life of 175 years

Q: If GE sells 330 ovens, how many ovens in total would they expect to provide a full or partial refund…

A: The lifespan of an oven made by General Electric (GE) has a mean life of 2.03 years, exponentially…

Q: Element X decays radioactively with a half life of 9 minutes. If there are 170 grams of Element X,…

A: Given- Element X decays radioactively with a half life of 9 minutes and there are 170 grams of…

Q: The United States had an economic growth rate of approximately 2.9%and GDP of approximately $20.58…

A: Given query is to find the GDP in 2021.

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.