Che amount of carbon 14 present in a paint after t years is given by A(t) = A, e The paint contains 29% of its carbon 14. Estimate the age of the paint. The paint is aboutyears old. (Round to the nearest year as needed.)

Q: Radioactive substances decay at a rate proportional to the amount, i.e.  dN/dt = −kN  with k a…

A:

Q: Radioactive Carbon-14 The percentage Pof radioactive carbon- 14 remaining in a fossil after t years…

A: Note: As P and b for the first question are not given in the data provided by you. Solved the second…

Q: The rabbit population at the city park increases by 5% per year. If there are intially 454 rabbits…

A: A)Population y in terms of y is given as;y(t) =P0 (1+r)t P0=454 r=0.05 y(t)=454 (1.05)t

Q: The intensity of the reaction to a certain drug, in appropriate units, is given by R(t) = te -0.1…

A:

Q: The growth rate of a population, in people per year, is given by r(t) = Aekt with k > 0, t in years…

A:

Q: keletal remains of the so-called "Pittsburgh Man," unearthed in Pennsylvania, had lost 84% of the…

A: The bones lost 84% of the carbon 14 they originally contained. The formula used to calculate is Q(t)…

Q: The rabbit population at the city park increases by 3% per year. If there are intially 296 rabbits…

A:

Q: Radioactive iodine decay Radioactive iodine 131I is fre- quently used in tracer studies involving…

A: Solution: Consider the given formula for radioactive iodine decay is: A(t) = A0a-t where A0 is the…

Q: Half-life of an element is the time required for half of a given sample of radioactive element to…

A: Given the radium has a half life period of 1600 years and initial concentration of Radium in a…

Q: Population growth The population of Silver Kun in the year 1890 was 6250. Assume the population…

A: Given- The population of silver run in the year 1890 was =6250 (Initial Value) Population increased…

Q: The daily cost C (in dollars) for a manufacturer to produce x electronic video components is given…

A: We will use given expression to find the solution.

Q: 20. A model that can be used for predicting the height H (in cm) of a child based on his or her age…

A: The height of a x year old child is given by the function: H(x)=70.228+5.204x+9.222 ln x

Q: 2. A triangle has a height that is increasing at a rate of 2 cm/s, and its area is increasing at a…

A: Area of the triangle , A =12(Base)(Height) Product Rule of Differentiation : du.vdt=u.dvdt+dudt.v

Q: 33. The half-life of radium-226 is approximately 1,600 years. Step 1. Determine a so that A(t) =…

A: topic - exponential function

Q: A population grows according to the model, 1400 e 0.06t where A is the population t years after the…

A: Given,Population functionA(t)=1400e0.06twhere A is the population after t yearsTreating 2000 as…

Q: The half-life of radium-222 is approximately 38 seconds. Step 1 of 3: Determine a so that A(t) =…

A: NOTE: Refresh your page if you can't see any equations. . here half-life is 38 seconds,  so when…

Q: The rate of decay of radium is proportional to the amount present at any time. The half-life of…

A: The understanding of radioactive decay is required. The explanation part is given below.

Q: When a plant dies, it stops acquiring carbon-14 from the atmosphere. The amount y (in grams) of…

A:

Q: Strontium-90 has a half-life of 28 days.(a) A sample has a mass of 50 mg initially. Find a formula…

A: (a) A sample has a mass of 50 mg initially. Find a formula for the mass remaining after t days.Let…

Q: The area covered by a certain population of bacteria increases according to a continuous exponential…

A: An exponential growth model is of the form y=A0ert

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

A: Given: The population (P) of a community is known to increase at a rate proportional to the number…

Q: 39. A population P, grows at the rate P'(t) = 5(t +1) In /t +1 thousand individuals per year at time…

A: Given population growth at time t  is  P't=5t+1lnt+1 Then…

Q: Starting with an initial value of P(0) = 50, the population of a prairie dog community grows at a…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: The rabbit population at the city park increases by 11% per year. If there are intially 311 rabbits…

A: Initially, there are 311 rabbits. Population increases 11% per year and that means 111% of the total…

Q: The motion of an particle follows an exponential function s(t)=et. (a) Determine the velocity of the…

A: If the distance function is differentiated with respect to the time, then the velocity function is…

Q: A model for the ability M of a child to memorize, measured on a scale from 0 to 10, is given by M =…

A: Given - A model for the ability M of a child to memorize, measured on a scale from 0 to 10, is given…

Q: The amount of a radioactive isotope present at time t is given by A(1) = 500 e 002631 present is 500…

A: Amount of radio active isotope present after t year is given as an exponential function.  The…

Q: The growth rate of a town's population after t years is P'(t) = 420 t². If the town's current…

A:

Q: Decay Rate, k 6.7% per year = -0.067 Complete the table shown to the right for the half-life of a…

A: The table given is                                       Half-Life…

Q: Eliminate the arbritrary constant/s. Show full solution. x = -ln t, y= at + bt2

A:

Q: 3. During an economic recession, a firm decides to decrease its output, y, at a constant relative…

A: Let the annual percent rate of decrease in the firm’s output to achieve this target be r.

Q: 1. A community experiences linear population growth at a yearly rate of 3%. The population in 2000…

A:

Q: Heighr (in cm)25.6 11 Based on the information he has gathered: a. What is the average weekly…

A:

Q: 1. The price of a new machine is $14,000. After ten years, the machine has a salvage value of $750.…

A: Linear model  where, b = y intercept = starting value = $ 14,000

Q: 10. A bacteria culture contains 300 cells initially and grows at a rate proportional to itrs size.…

A:

Q: 2. There is a pond on my property that Wildlife and Fisheries stocks. From information provided to…

A: Given:- 2. There is a pond on my property that Wildlife and Fisheries stocks. From information…

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

A: Please see the answer below

Q: 8) The amount of pollution in a certain lake is P(t) = PLOD= [ ++3) ₁V where t is measured in years…

A: The given amount of pollution in a certain lake is Pt=t14+33, where t is measured in years and P is…

Q: Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 150…

A:

Q: A strain of bacteria has a growth rate that is propor­tional to the size of the population.…

A: a. Given growth rate if proportional to the size of population. Hence, Simplifying the differential…

Q: . Radioactive Decay A 15-g sample of radioactive iodine decays in such a way that the mass remaining…

A: Given: mt=15e-0.087t To Determine: How many days the mass remaining is 5 grams

Q: lation of 450 bacteria is introduced into a culture and grows in number according to the equation…

A:

Q: The half-life of phosphorus-32 is approximately 24.3 days. Step 1 of 3: Determine a so that A(t) =…

A: Given : Half life time of phosphorus- 32 = 24.3 days

Q: Radioactive Carbon-14 The percentage P of radioactive carbon- 14 remaining in a fossil after t years…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Dinosaur fossils are often dated with radioactive 40 potassium 4°K. The half-life of potassium K is…

A:

Q: II. Simple Chemical Conversion Radium decomposes at a rate proportional to the quantity of radium…

A: Given the data

Q: An initial investment amount P, an annual interest rate r, and a time t are given. Find the future…

A: The future value of the investment when interest is compounded continuously.

Q: A population of mosquitoes decreases exponentially. The size of the population. P, after t days is…

A:

Q: t/1620 The half-life of radium-226 is 1620 yr. Given a sample of 1 g of radium-226, the quantity…

A:

Q: 10. A bacteria culture contains 300 cells initially and grows at a rate proportional to itrs size.…

A: NOTE: As per our company guidelines, we are supposed to answer ?️only the first 3️⃣ sub-parts.…

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.