Let Q represent a mass of carbon 14 (14C) (in grams), whose half-life is 5715 years. The quantity of carbon 14 present after t years is given by the following. Q = 4(1/2)^(t/5715)   (a) Determine the initial quantity (when t = 0). ____________ g (b) Determine the quantity present after 1500 years. (Round your answer to two decimal places.)  _____________g

Q: 9) A rectangular swimming pool has a base that is 10m by 20m. Water is being pumped into the pool at…

A:

Q: The half-life of palladium-100 is four days. (So half of any given quantity will disintegrate in…

A: Let the initial mass of palladium-100 is m, it is given that mass will reduced to half in 4 days. so…

Q: At the beginning of an experiment, a scientist has 332 grams of radioactive goo. After 90 minutes,…

A: Given A Scientist has 332 grams of radioactive goo.  After 90 minutes, her sample has decayed to…

Q: Radium disintegrates at a rate proportional to instantaneously present. If the half - life of…

A: Let the amount of Radium after t years be given by R(t). The rate of disintegration is dRdt.…

Q: The half-life of a radioactive material is the time required for an amount of this material to decay…

A: Solving the differetial equation: Q'=-rQ

Q: 41. Time Required to Reach a Goal How many years will it take for an initial investment of $10,000…

A: Consider that the initial investment of $10,000 compounded annually to grow to $25000, with rate of…

Q: A 200 g sample of radioactive polonium-210 has a half-life of 138 days. This means that every 138…

A:

Q: A population of cattle is increasing at a rate of 800 + 80 t per year, where t is measured in years.…

A:

Q: At the beginning of an experiment, a scientist has 252 grams of radioactive goo. After 120 minutes,…

A:

Q: At the beginning of an experiment, a scientist has 180 grams of radioactive goo. After 210 minutes,…

A:

Q: At the beginning of an experiemnt, a scientist has 348 grams of radioactive goo. After 255 minutes,…

A:

Q: Heather wants to invest $35,000 of her retirement. She can invest at 4.8% simple interest for 20 yr,…

A: Simple interest is applied only on the principal amount every year. The interest amount accumulated…

Q: 2. Bacteria grow in a nutrient solution at a rate proportional to the amount present. Initially,…

A:

Q: Radon-222 has a half-life of 4.00 days. Given its mass 5.937 gram at a certain time, what was the…

A: We will find out the required value.

Q: $8,000 is invested in an account earning 8.7% interest (APR), compounded continuously. Write a…

A: Solution

Q: $5,600 is invested in an account earning 9.1% interest (APR), compounded continuously. Write a…

A:

Q: A radium isotope decays exponentially and its half-life is 1600 years. Using the equation A(t)…

A: Given Half time = 1600 years At=A0e-kt

Q: 3. The population of a community is known to increase at a rate proportional to the number of people…

A: Let initial population P0Population at time t is P.

Q: A cell culture contains 12 thousand cells, and is growing at a rate of r(t) = 2e0.17t thousand cells…

A:

Q: Solve Using Dn/dt. A certain radioactive material is known to decay at a rate proportional to the…

A: We will construct a differential equation according to the given conditions and solve it using…

Q: Revenues from a manufacturing operation flow continuously into a firm's treasury at a rate of Ax)…

A: As per Bartleby's answering policy, we can answer only one question. So here we have solved the…

Q: The growth rate of the bacterium, a common bacterium found in the human intestine, is proportional…

A: From the problem, we know that -The growth rate of the bacterium found in the human intestine is…

Q: A wolf population is growing at a rate of 9.3% per year. Find the time at which the wolf population…

A:

Q: 2. Carbon decays at a rate proportional to the amount present. The percentage lost is 5% in 150…

A:

Q: Radon-222 has a half-life of 4.00 days. Given its mass 3.055 gram at a certain time, what was the…

A:

Q: 3. After 4 days, 25 g of radioactive substance is present. Five days later, 15 grams is present. a.…

A: Topic:- exponential decaying function

Q: Radon-222 has a half-life of 4.00 days. Given its mass 2.789 gram at a certain time, what was the…

A: We will find out the required value.

Q: Solve for x accurate to three decimal places. ln x2 = −8

A: ln x2=-8ConceptIf ln a=ba=eb

Q: 13. A motorcycle is moving at 30 m/s when the rider applies the brakes, giving Che motorcycle a…

A: Consider the given information. If the acceleration is constant then we can use these equations.…

Q: at a constant 3. The surface area of a balloon being inflated changes a rate. If initially, its…

A:

Q: A sample of 400 g of radioactive lead-210 decays to polonium-210 according to the function A(t) =…

A:

Q: Find the missing values assuming continuously compounded interest. (Round your answers to two…

A:

Q: cteria grow in a culture at a rate proportional to the amount present. Initially, 300 ands of the…

A:

Q: POMERO OF 10 al rate of 0.9% compounded continuously, how long to the nearest year) would take b the…

A: Given Population P=6.4 billion , r=0.9%

Q: lodine-131 is a radioactive that has a pretty short half life of only 8 days. A sample of lodine 131…

A: Radioactivity equation:                                A = Aoe-λt                      Where, Ao is…

Q: The half-life of a radioactive substance is 160 years. a) Compute the decay constant k (4 decimal…

A: a)Half-Life of a radioactive substance is 160 years, Initial amount=300 g time, t=160 years,We know…

Q: If human toenail grows at an average rate of about 0.13 inch a month.   1 year has 12 months. 1…

A: Given, Growth of human to nail =0.13 inch/month 1 year has 12 months. 1 inch is equal to 2.54 cm.…

Q: At the beginning of an experiment, a scientist has 316 grams of radioactive goo. After 240 minutes,…

A:

Q: A cell culture contains 10 thousand cells, and is growing at a rate of r(t)=11e0.06tr(t)=11e0.06t…

A: A cell culture contains 10 thousand cells, and is growing at a rate of r(t)=11e0.06tr(t)=11e0.06t…

Q: The population of student in a University grows at some specific rate at time t. After (ln 40) hours…

A: Suppoose  rate of population growing = r Initial population = P0 The population growth is given by…

Q: A wooden artifact from an ancient tomb contains 65% of the carbon-14 that is present in living…

A: the radioactive decay equation is  given by m=m0e-ln2t't where t' is the half life. the tomb…

Q: The population growth rate is 3.0% per day with a current population of 30,000.            a.…

A:

Q: find the present value of $10000 at the end of 25 years if money can be invested at 12% with…

A: We will use the compound interest formula to find the present value

Q: Radon-222 has a half-life of 4.00 days. Given its mass 5.488 gram at a certain time, what was the…

A: Given that, Radon-222 has a half-life of 4.00 days. Given its mass 5.488 gram at a certain time We…

Q: 3. After long study, tree scientists (dendrologists) conclude that a eucalyptus tree will grow at a…

A: Given : A eucalyptus tree will grow at a rate of 0.6+4t+13 feet per year , t is time in years.…

Q: (a) After 20 years, 15% of the initial mass of the radium has decayed. (i) Find the half-life period…

A:

Q: At the beginning of an experiment, a scientist has 196 grams of radioactive goo. After 210 minutes,…

A:

Q: Radon-222 has a half-life of 4.00 days. Given its mass 3.168 gram at a certain time, what was the…

A: We will find out the required solution.

Q: A 631-kg elevator starts from rest and moves upward for 3.30 s with constant acceleration until it…

A: Step:-1 Part (A):- Average power = Force (F) × Average Velocity (vavg.) Given that elevator starts…

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.