A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function  m(t) = 13e^-0.011t where m(t) is measured in kilograms. (a) How much of the mass remains after 44 days? (Round your answer to one decimal place.)

Q: A sample population of strands of the bacteria is increasing at rate proportional to the population.…

A:

Q: A certain radioactive material decays at a rate proportional to the amount present. At time ?=0,…

A:

Q: 4. A hazardous material was found to decay at a rate proportional to the amount present. Initially,…

A:

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

A: given,     radioactive material is decay at a rate proportional to the amount present .initially 50…

Q: What is the total amount of 24000 TL with 4,8 % continuously compound interest after 5 years?

A: Consider the formula for continuous compounding, A=P·er·tHere,P=principalr=rate of interestt=time…

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

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

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

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

Q: A certain radioactive element decomposses at a rate proportional to the amount present. If 100…

A:

Q: What is the total amount of 4500 TL with 3,7 % continuously compound interest after 3 years?

A: Given Present value (P)= 4500 TL Rate (r)=3.7% Number of years (t)= 3

Q: Radiocarbon dating is a method used by scientists to estimate the age of ancient objects that were…

A:

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

A:

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

A:

Q: A quantity with an initial value of 200 grows continuously at a rate of 55% per day. What is the…

A: Let the quantity Pn grown continuously at a rate of 55% per day. Initial quantity is P0=200.

Q: An experimental forest is to be grown by planting 3000 trees each year on the same day of the year.…

A: Let i = number of years = 0, 1, ... , 10 and the number of trees planting in the starting of each…

Q: Suppose income from an investment starts (at time 0) at $6000 a year and increases linearly and…

A: While calculating compound interest, the addition of interest to the principal sum of a loan or a…

Q: A quantity with an initial value of 840 decays continuisly at a rate of 5% per day. What is the…

A:

Q: A bacteria culture starts with 4 bacteria and grows at a rate proportional to its size. After 2…

A:

Q: Radioactive cesium-137 has a half-life of 30.17 years. How much of an initial amount of 1,000…

A: If N0 is the initial amount and t is the number of years then equation of decay  is given by…

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

A:

Q: A quantity with an initial value of 850 grows continuously at a rate of 90% per decade. What is the…

A: Given: A quantity with an initial value of 850 grows continuously at a rate of 90% per decade. To…

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

A:

Q: The radioactive isotope lead has a half-life of 3.3 hours and decays at a rate proportionate to the…

A: This is a problem of differential equation and integration. Based on the given scenario first of all…

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

A:

Q: Determine the growth constant of a population that is growing at a rate proportional to its size,…

A: Consider the population size is given as P(t). The expression for the exponential growth rate is…

Q: A quantity with an initial value of 200 grows continuously at a rate of 4% per second. What is the…

A: To find: The value of quantity after 1.55  minutes. Given: The initial value of quantity is 200 and…

Q: A radioactive element is known to decay at a rate proportional to its present mass. Initially, there…

A: Given: A radioactive element is known to decay at a rate proportional to its present mass.…

Q: A quantity with an initial value of 8200 grows continuously at a rate of o.55% per decade. What is…

A:

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

A:

Q: Find the amount after 3 years if $ 1000 is invested at an intrest rate of 12% per year, compounded…

A: Given :             The amount invested is $1000.             Interest rate = 12% per year.…

Q: A radioactive substance decays at a continuous rate of 17% per day.  After 8 days, what amount of…

A:

Q: A quantity with an initial value of 310 grows continuously at a rate of 8.5% per second. What is the…

A:

Q: A certain radioactive substance decomposes at a rate proportional to the amount present. Of the 1000…

A:

Q: A radioactive material decays at a rate proportional to its amount. If the material has a half-life…

A: model is  A=A0ektfor half-life put A=A02thenA02=A0ektsolving for t, we get k=-ln(2)t

Q: A quantity with an initial value of 870 decays continously at a rate of 0.75% per day. What is the…

A:

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

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

Q: a spherical snowball is melting in such a way that its surface area decrease at the rate of…

A:

Q: A colony of bacteria with originally 100 cells has now grown to 900 in 2 hours. Assuming the rate of…

A:

Q: A radioactive element is known to decay at a rate proportional to its present mass. Initially, there…

A: An ordinary differential equation is an equation containing independent variables, dependent…

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

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: In March 1976 the world population reached 4 billion. At that time, a popular news magazine…

A:

Q: The number of bacteria in a certain population increases according to a continuous exponential…

A:

Q: The half-life of plutonium 239 is 24,200 years. Assume that the decay rate is proportional to the…

A:

Q: A radioactive element decays according to the function Q=Q, e", where Q, is the amount of the…

A: We will solve the problem

Q: Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved.…

A: 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left.

Q: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time…

A: Given- Half life t12 =3.3 hours, Intial weight=1 gm. To find- The time in which the radioactive…

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.