The half-life of iodine-123 is about 13 hours. You begin with 52 grams of iodine-123.   (a) Write an equation that gives the amount of iodine-123, I, remaining after t hours. Write your answer in the form I(t)=a⋅bt.   Round your answer for b to three decimal places.   I(t)=       (b) Determine the number of hours needed for your sample to decay to 7 grams.   Round your answer to the nearest integer.   It takes.                hours for the sample to decay to 7 grams.

Q: A radioactive substance decays according to the equation N = 105 e SIA where N is the number of…

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present.…

A: Here, initial mass =50 mg rate is proportional to the amount.m=50e-0.053t dmdtαm

Q: The half-life of a substance is found by using the equation A(t) = A0e−kt   where A(t) is the…

A: GIven: Half life of a substance is given by equation: A(t) = A0e−kt   where A(t) is the amount…

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

A: Assuming continuous compounding P=P0eKt P→Population at moment in time P0→initial Population…

Q: Suppose the quantity (in grams) of a radioactive substance present at time t isQ(t) =…

A: Radioactive substances have different rates of decomposition.

Q: The annual world rate of water use t years after 1960 for t<35 was approximately 860 e^.04t cubic…

A: We have given the annual world rate of water use t years after 1960 for t&lt;35 was approximately…

Q: the decay of 10 grams of a substance is given by the equation A=10(0.76)t where t is in hours.how…

A: To use the exponential model for decay to determine the required time .

Q: From the beginning of the year 2000, the annual world demand for oil has increased. To account for…

A: Rate of oil production is, D(t) = 3.8e0.04t billions of barrels per year where t is the number of…

Q: 0,000. The co 20% of its me sales, 75% are le and the rema

A: Calculation of January Cash collections from sales as,

Q: The amount of a radioactive isotope present at any time (t in years) is given by the equation A (t)…

A: Given, A(t)=250 e-0.045t

Q: A sample of 800 g of an isotope decays to another isotope according to the function A(t)= 800 e…

A:

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

A: Given  400 g of radioactive lead-210 decays to polonium-210 according to the function…

Q: A radioactive substance decays according to A=A0e^−0.0048t, where A0 is the initial amount and t is…

A:

Q: The half-life of selenium-72 is 8.4 days. How long will it take for 20g to decay to 15g?

A: NOTE: Refresh your page if you can't see any equations. . here the half-life is given so use the…

Q: A species of rabbits has a growth rate of 0.625 a month. If a population of foxes inhabits the same…

A: Given Growth rate of rabbits = 0.625 a month Foxes kills 10 rabbit per day

Q: Radium decomposes in air at the rate proportional to the amount present. It is found out that in 25…

A: The decomposition rate of the radium in air is proportional to the amount present in air.

Q: A bacterial population starts with 400 bacteria and grows at a rate of r(t) = (450.266)e12567t…

A: I have given solution in step2

Q: Suppose the quantity (in grams) of a radioactive substance present at time t is Q(t) = 432 (3-0.3),…

A: Given query is to find the amount of radioactive after 4 months and time taken to reach 16 grams.

Q: A toxin is introduced into a colony of bacteria, and t hours later, the population of the colony is…

A: Given that a toxin is introduced into a colony of bacteria and t hours later the population of the…

Q: A certain radioactive substance has a half-life of 38 hours. The rate of change in the decay is…

A: In this we are going to use decay formula so I'm providing hand written solution for this

Q: The half-life of strontium-90 is 28 years. How long will it take a 50-mg sample to decay to a mass…

A: Introduction: The half-life is the amount of time it takes for a quantity to decline to half its…

Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

A:

Q: The concentration of an antihista-mine in the bloodstream of a healthy adult is modeled by C = 12.5…

A: 6 hour period means from t=0 to t=6That is from start of the medication  to 6 hours after medication…

Q: Given that X ~ Exp(0.7), find the decay rate.

A: Given that X ~ Exp(0.7).

Q: How long will it take is sample of radioactive substance to decay to half of its original amount, if…

A: Find the time t.

Q: A certain species of deer is to be introduced into a forest, and wildlife experts estimate the…

A: It is given that A certain species of deer is to be introduced into a forest, and wildlife experts…

Q: A sample of 500 g of radioactive​ lead-210 decays to​ polonium-210 according to the function…

A: Given function  A(t)=500e−0.032t Here, A(t) is the amount of radioactive lead and t is the time in…

Q: The half-life of a substance is found by using the equation A(t) = A0e−kt where A(t) is the amount…

A: NOTE: Refresh your page if you can't see any equations. . the given equation is  where A0 is the…

Q: A drug is injected into a patient’s bloodstream and t seconds later, the concentration of the drug…

A: C (t) = 0.25 (1 + 7e-.05t) We ahve to find t when C(t) = 0.35

Q: A mass of 100 grams of a particular radioactive substance decays according to the function m(t) =…

A:

Q: At the beginning of an experiment, a scientist has 340 grams of radioactive goo. After 255 minutes,…

A:

Q: The value of a computer t years after purchase is V(t) = 2, 000e-0.35t dollars. At what rate is the…

A:

Q: The population of a certain inner-city area is estimated to be declining according to the model…

A: NOTE: Refresh your page if you can't see any equations. . take t=66 years

Q: When a vertical beam of light passes through a transparent medium, the rate at which its intensity I…

A:

Q: Q.4 Suppose that electricity is draining from a capacitor at a rate that is proportional to the…

A:

Q: A certain radioactive substance has a half-life of 38 hours. The rate of change in the decay is…

A: Solved below

Q: An initial amount of 100 g of the radioactive isotope thorium-234 decays according to Q(t) =…

A:

Q: The sales decay for a product is given by S= 80,000e^-0.3x, where S is the monthly sales and X is…

A: A) S(x)= 80,000(e^-0.3x) Given x= 2 S(2)= 8000×(e^(-.3*2)) S(2)= $ 4390.493089

Q: The population of a certain inner-city area is estimated to be declining according to the model…

A: Given: The population decline of a certain city is given as, P(t)=580000e-0.022t t- Number of years…

Q: Water is pumped out of a holding tank at a rate of 3-3e-0.5t liters/minute, where t is in minutes…

A:

Q: The size of a stray cat population at the bay area of a certain city grows at a rate of 7% monthly.…

A:

Q: The mass of a radioactive sample is given by M(t)=M010^-kt where t is the time in years, M0 is the…

A:

Q: A radioactive substance decays according to A=A0e^−0.0037t, where A0 is the initial amount and t is…

A:

Q: A thermometer is taken out of a room at 64 ° F, outside where the temperature is at 8 ° F. After…

A:

Q: A 200-gal tank is half full of distilled water. At what time (t) = 0, a solution containing 0.5…

A: A 200-gal tank is half full of distilled water. At what time (t) = 0, a solution containing 0.5…

Q: Blood carries a drug into an organ at a rate of 3 cm3/sec and leaves at the same rate. The organ has…

A: Exponential growth/decay is given by dxdy=rici-r0vx here, ri=3= rate of drug entering. and r0=3=…

Q: The doubling period of a bacterial population is 2020 minutes. At time t=110t=110 minutes, the…

A:

Q: From the beginning of the year 2000, the annual world demand for oil has increased. To account for…

A: We need to find estimated years and oil barrels.

Q: A biologist is researching a newly discovered species of bacteria. At time t = 0, he puts 200…

A: (a) Let the initial number of bacteria be a. The number of bacteria at any time t be P(t) and time…

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.