Suppose an Egyptian mummy is discovered in which the amount of​ carbon-14 present is only about two​-fifths the amount found in living human beings. The amount of​ carbon-14 present in animal bones after t years is given by y=y0e^−0.0001216t​, where y0 is the amount of​ carbon-14 present in living human beings. About how long did the egytptian die?

Q: Suppose a small quantity of radon gas, which has a half-life of 3.8 days, is accidentally released…

A: half life problem

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

A: Given that the​ half-life of​ carbon-14 is 5600 years and if a piece of charcoal made from the wood…

Q: A certain radioactive element decays over time according to the equation where 4= the number of…

A: Solution attached below

Q: Suppose the population of a certain bacteria in a laboratory sample is 100. If it doubles in…

A: The initial population of the bacteria is, P0=100. After every t=6, the population doubles. So, the…

Q: suppose the half-life of caffeine in the bloodstream of a healthy adult is 6 hours. If the person…

A: Given: initial quantity of caffeine C0=200 mgt=12 hrs (11 am to 11 pm)half life t12= ln 2K…

Q: odine -131 has a half-life of approximately 8 days. ind the amount of iodine-131 left from a 100…

A:

Q: To get $800 after 212years at 8% compounded continuously

A: $800 after 212 years at 8% compounded continuously.

Q: The half-life of carbon-14 is 5700 years. If an item is discovered with only 17% of the original…

A: Given Half life of carbon-14 =5700 years  i.e. and an item is found with only 17% of the original…

Q: A radioactive substance has a half-life of 64 hours. If 200 grams of the substance are initially…

A:

Q: The half-life of carbon-14 is 5730 years. How long does it take for 3.4 grams of carbon-14 to be…

A: We have to find

Q: How long does it take for $350 to grow to $840 at 6% annual percentage rate compounded continuously…

A: Continuously compounded interest formulaA= PertP = the initial principlee = natural baser = annual…

Q: After 2250 years, 25% of a radioactive material remains. If the rate of decay of the material is…

A: Half-life = 0.693/Decay constant(lambda)

Q: Most smoke detectors contain a tiny amount of Americium-241, which is an artificially produced…

A: Assuming that the radioactive decay follows exponential distribution, the quantity of substance…

Q: If there are 520 grams of Tadioactive material with a half-life of 12 hours, how TIuch of the…

A: The material is decaying at a constant rate, every 12 hours it is getting halved.  So, it is an…

Q: Today there are 500 ants on an colony. They breed with a constant continuous growth rate of 20% per…

A: We will find out the required solution.

Q: What is the half-life of a radioactive substance if it takes 5 years for one-third of the material…

A: We have to find half life period

Q: If a Paramecium is about 390 micrometers long, how many centimeters is it? Express in real numbers…

A:

Q: solve for y: ln(3-y)-ln(y) = 2x + ln(5) without a calculator

A: Given equation is :Moving all the logarithm terms and using the property: ln(a) – ln(b) =…

Q: The half-life of Cesium-137 is 30.7 years. How long will 200 grams of Cesium-137 take to decay to…

A: Given data The half-life of the cesium-137 is t1/2 = 30.7 years. The initial amount of the…

Q: A bank pays interest continuously at the rate of 6%. How long does it take for a deposit of Q0 to…

A:

Q: A material decays at the rate of 0.099% per year. How long will the material take so that only 30%…

A:

Q: Suppose you have a 1024 mg sample of a substance known to have a half-life of 50 years. Find the…

A: Given half-life of sample=50 yrs and the initial sample is = 1024mg.

Q: How long will it take for $4000 to double in value if it is deposited in an account bearing 7%…

A: Continuous compound interest formula: A=Pert P-principle A-Amount r-rate t-number of years.

Q: Interest is compounded continuously at 5%.  How long until a $5000 investment grows to $12000?

A: Interest is compounded continuously at 5% $5000 investment grows to $12000

Q: The half-life of carbon-14 is 5730 years. How long does it take for 3.9 grams of carbon-14 to be…

A: h=5730 years. x=final amount=1.7 grams. y=initial amount=3.9 grams. t=h(ln(x/y))/ln(1/2)…

Q: The half-life of plutonium-241 is approximately 13 years. How much of a sample weighing 4 g will…

A: The half-life of plutonium-241 is 13 years. We have to find how much sample of 4 g will remain after…

Q: Suppose you have 100g of Titanium-44, which has a half-life of 63 years. After how long will only 1g…

A: Initial amount=P=100  Half life= H= 63 years  Final amount= A= 1  Time= t years Using the half-life…

Q: Jose invests $10,000 at 10% interest that is compounded continuously. Which is the value after 10…

A: We have to find compound amount

Q: A scientist begins with 450 grams of a radioactive substance. After 55 minutes, the sample has…

A:

Q: Of an initial amount of 8000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

A:

Q: A quantity with an initial value of 590 decays exponentially at a rate such that the quantity cuts…

A: A quantity with an initial value of 590 decays exponentially at a rate such that the quantity cuts…

Q: A toxic radioactive substance in the amount of 7 miligrams per square centimeters is detected in the…

A:

Q: A sample of a radioactive substance decayed to 10% of its original amount after 30 years. What is…

A: Given After 30 years substance decayed to 10 % of its original amount

Q: How long, to the nearest year, will it take an investment to triple if it is continuously compounded…

A: We can find the required year in the following steps.

Q: If 100 grams of a radioactive material diminish to 80 grams in 2 years, find the half-life of the…

A: Let the given condition can be modeled as  y=y0eλt   where, y=  Final quantity y0= Initial quantity…

Q: Aman with $30,000 to invest decides to diversity his investments by placing $15,000 in an account…

A:

Q: An accidental spill of 65 grams of radioactive material in a local stream has led to the presence of…

A:

Q: $2000 is invested in an account that pays interest compound continuously, how long will it take to…

A: The answer is given below:

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

A:

Q: Suppose that we initially have 500 mg of a radio-active substance as sample. After a year, the…

A:

Q: A quantity with an initial value of 8200 grows continuously at a rate of 0.55% per decade. What is…

A: Initial Value=  8200. Growth rate= 0.55% . We can formulate the following equation for "t" years :…

Q: The half-life of Carbon-29 is 1300 years. If 15 grams are present now, how much will be present in…

A: Let A(t) be the amount of Carbon-29 remaining in t years, then

Q: An unknown radioactive element decays into non-radioactive substances.  In 660 days the…

A:

Q: A radioactive substance has a half-life of 25 years. If 640 grams of the substance are present…

A:

Q: Suppose a small quantity of radon gas, which has a half-life of 3.8 days, is accidentally released…

A:

Q: The half-life of carbon-14 is 5730 years. How long does it take for 2.1 grams of carbon-14 to be…

A: A(t)=A0(1/2)t/h h is the half life A0 is the initial value

Q: In the last 4 line, where is the ^2 in the ln part?

A: The given integral,      ∫13arctanx dx

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

A:

Q: Of an initial amount of 7000 g of lead-210, how much will remain in 180 years? Lead-210 decays at a…

A: Given that: Initial amount of lead, P0=7000gRate of decay, k=3.15%per year.

Q: The half-life of radium is 1690 years. If 150 grams is present now, how long (to the nearest year)…

A: The half-life of radium is 1690 years. If 150 grams is present now, how long (to the nearest year)…

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.