The half-life of radium-226 is 1590 years. (a) If a sample has a mass of 150 mg, find a function that models the mass that remains after t years. (b) Find the mass that will remain after 1000 years. (c) After how many years will only 50 mg remain?

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

A: a: it doubles in every 30 minute and initial population = 10 then we can write the function as:…

Q: Suppose $15000 is invested at 7% interest compounded continuously. How long will it take for the…

A: Suppose $15000 is invested at 7% interest compounded continuously. How long will it take for the…

Q: The average profit a local store owner earns on a given day is $810 and is growing exponentially at…

A:

Q: A culture contains 1400 bacteria initially and doubles every 50 minutes. Assuming that the rate of…

A: Consider the function that models the number Pt=Aekt=B2tC Here, the objective is to find the…

Q: The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A: Given : S=the amount of radium you start with=250gm t=the amount of time in years=950 years  h=the…

Q: Suppose an Egyptian mummy is discovered in which the amount of​ carbon-14 present is only about…

A: The amount of carbon-14 present in animal bones after t years is given by the equation:…

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 population of bacteria is initially 8000. After three hours the population is 4000. If this rate…

A: Given,          A population of bacteria is initially 8000. afters three hours the population is…

Q: A culture of bacteria is known to grow at a rate proportional to the present amount. After one hour…

A:

Q: How long will it take for an investment of $1000 to double in value if the interest rate is 8.5% per…

A:

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

A: (a) Given: The initial population is 500. The number of cells in a culture doubles approximately…

Q: The derivative of an exponential function isn't always another exponential function.

A: Derivative of an exponential function is given by :ddxef(x,y,z) = ef(x, y , z). ddxf(x, y , z)

Q: Suppose that 50,000 bacteria are in a dish and that the population grows continuously by 4% each…

A:

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

A:

Q: Consider the following situation. A tank contains 2500 L of pure water, with 15 kg of salt dissolved…

A: Let consider that function s(t) is kgs of salt in the tank at time t minutesAs we know thats'(t)=The…

Q: Total reserves for a non renewable resource at 250 million tones.annual  consumption, currently at…

A: We have total non renewable resources=250 million tonesfirst year consumption is 20 millionsecond…

Q: The population of a certain municipality increases at the rate proportional to the present…

A: Here we solve the given population growth problem.

Q: f) The population of a town grows at the rate of 3% per year (compounded continuously). How long…

A:

Q: At the time of the birth of a child, a parent wants to begin a college fund that will grow to $43000…

A: Given that the interest is compounded continuously

Q: The population of an island grows at a rate proportional to its population. If the growth rate is 5%…

A:

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

A:

Q: Suppose an Egyptian mummy is discovered in which the amount of​ carbon-14 present is only about…

A: Given: y=y0e-0.0001216t

Q: The rate of change of the male population of a particular barangay is proportional to the male…

A:

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

A:

Q: For a period of time, an island's population grows at a rate proportional to its population. If the…

A: The general growth formula is given by,

Q: In a laboratory experiment, the population of bacteria in a petri dish started off at 380 and is…

A:

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

A: The amount remaining after hours 24 hours is 88.5 milligrams.

Q: When $1000 is invested at r% interest (compounded continuously) for 10 years, the balance is f (r)…

A: Consider that $1000 is invested at r% interest compounded continuously for 10 years. Calculate the…

Q: At time t years an industry consumes fuel at the rate of /(2t + 9) million barrels per year. If the…

A: Linear equation are those equation in which highest power of the variable is 1. The linear equation…

Q: The number of users on a website is 490 and is growing exponentially at a rate of 65% per year.…

A:

Q: Radium decomposes at a rate proportional to its present radioactive. In 100 years, 100 units of…

A:

Q: An Asian country had a population of about 0.90 Billion people in 1995 and a growth rate of 1.3% per…

A: *** This is the problem related to financial mathematics and we are advanced math expert and have…

Q: The number of bacteria in a liquid culture is observed to grow at a rate proportional to the number…

A: We know that at the beginning of the experiment, number of cells = 104 After 3 hours of the…

Q: Three thousand dollars is deposited in the bank at 4% interest compounded continuously. What will be…

A: It is given that Money in the account $3000 Interest rate   We have to find the average value of…

Q: The value of a savings bond is growing by 2.8% per year compounded continuously. At this growth…

A:

Q: After 4.00 days, a sample of Uranium-237 decays to 66.4% of its original amount. Find: an expression…

A: Solve the given problem according to the given condition

Q: The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A:

Q: the number of bacteria in a certain population increases to a continuous exponential growth rate,…

A: NOTE: Refresh your page if you can't see any equations. . the given growth rate is  r=6.2%=0.062

Q: The growth rate of a bacteria culture is proportional to the number of bacteria present. If a…

A:

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

A: Given The number of cells doubles every 30 minutes. A) Initial Population =1000 B) Initial…

Q: An initial investment of $6000 grows at 5% per year. What function represents the value of the…

A: Given that initial investment made = $6000 It is said that the investment grows 5% per year. This is…

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

A:

Q: The population of an endangered species decreases at a rate of 7% per year. Approximately how long…

A: Answer

Q: Radium decomposes at a rate proportional to the amount present. In 100 yrs, 100 mg of radium…

A: Initial radium quantity Ni = 100 mg after t = 100 years N = 96 mg

Q: Suppose an unknown radioactive substance produces 6400 counts per minute on a Geiger counter at a…

A:

Q: The count in a bacteria culture was 600 after 15 minutes and 16054 after 35 minutes. Assume that…

A: Given that      The count in a bacteria culture was 600 after 15 minutes and 16054 after 35 minutes.…

Q: After 25 years, your savings account has now grown to $16,200 and has an interest of 6.1% that…

A:

Q: A certain bacteria culture is observed to double its amount after two hours it was initially…

A: Let say population is P. So population at time 't' is given by P(t). Assume initial population is P0…

Q: Find the time it takes for $5,800 to double when invested at an annual interest rate of 5%,…

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