If y(x) =2ke^(-2kx) for x>0 , then (x) = %3D

Q: Suppose a small quantity of radon gas, which has a half-life of 3.8 days, is accidentally released…

A: half life problem

Q: Pilar owns a parcel of land whose value tyears from now will be V (t) = 8000e" dollars. If the…

A: Given: Pilar owns a parcel of land whose value t years from now will be V(t) = 8000et dollars. The…

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

A: The differential equation for decay is dAdt=kA dAA=k·dt ⇒∫dAA=∫k·dt⇒lnA=kt+c1A=ekt+c1A=ektec1A=Cekt…

Q: What is the effective annual yield if a deposit of $1000 grows to $3300 in 12 years?

A: We know that the compound interest formula is  S=P1+rnnt where S is the amount after t years ,P is…

Q: A right triangle has legs of 30 inches and 40 inches whose sides are changing. The short leg is…

A:

Q: Find the effective rate of interest.; For 4% compounded continuously

A: 4% compounded continuously.

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: The surface area of kelp near Monterrey Bay is 40,000 square acres, but after four years a red sea…

A:

Q: The decay of radioactive elements can sometimes be used to date events from Earth’s past. In a…

A:

Q: how long will take for an investment to double in value if the interest rate 3% APR compounded…

A: We have A(t) = 2A(0) and r = 3% = 0.03

Q: Suppose the population of a certain bacteria in a laboratory sample is 100. If it doubles in…

A: The initial population of the bacteria is, P0=100. After every t=6, the population doubles. So, the…

Q: odine -131 has a half-life of approximately 8 days. ind the amount of iodine-131 left from a 100…

A:

Q: To get $800 after 212years at 8% compounded continuously

A: $800 after 212 years at 8% compounded continuously.

Q: Suppose the edges of a cube are increasing at a constant rate of 11 m/hr. Then, the volume of the…

A: Let the side of the cube = x Edges of the cube increasing rate dx/dt = 11 m/hr

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

A:

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: If the population of bacteria in a certain region triples in 30 days. In how many days will be three…

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Q: Suppose that a mothball loses volume by evaporation at a rate propotional to its instataneous area.…

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Q: Find the antiderivative of antiderivative of x2(ln(10x))2

A:

Q: If we know the rate of growth of a patch of moss, how can we calculate the area the moss covers?

A: The rate of growth of a patch of moss is modeled by a complex function A't, where t is measured in…

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: Find the time needed to double an investment at 8% annual interest rate compounded continuously.

A:

Q: solve for y: ln(3-y)-ln(y) = 2x + ln(5) without a calculator

A: Given equation is :Moving all the logarithm terms and using the property: ln(a) – ln(b) =…

Q: The area of the expanding rectangle is increasing at the rate of 48 square centimeters per second.…

A:

Q: The length of a rectangle is increasing at a rate of 5 meters per hour and the width is decreasing…

A: The length of a rectangle is 11 meters and the width is 20 meters. The length is increasing at a…

Q: If

A: Explanation and solutions is given below....

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

A:

Q: The original 24 m edge length x of a cube decreases at the rate of 2m/min.   When x=2 m, the…

A: Given,           The original 24 m edge length x of a cube decreases at the rate of 2 m/min.We know…

Q: A money market fund has a continuous flow of money at a rate of f(x)=0.07x+100 for 10 years. Find…

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: The population of Glenbrook is 375,000and is increasing at the rate of 2.25% per year. Predict when…

A: To find: When the population is 1 million. Given: Initial population is 375000 and rate of…

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

A:

Q: A right triangle has legs of 33 inches and 44 inches whose sides are changing. The short leg is…

A: to find:- dH/dt.

Q: see attached

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: If the radius of a right circular cylinder is increasing at a rate of 1 inch per minute, and the…

A:

Q: What initial investment at 8% compounded continuously for 5 years will accumulate to $50, 000?

A:

Q: Find the interest rate r needed for an investment of $5000 to grow to $8000 in 8 years if interest…

A:

Q: The length of a rectangle is decreasing at the rate of 1 feet per second, but the area remains…

A: Let x and y ( in feet ) be the length and width of rectangle and A ( in ft2) be the area of…

Q: how long will it take $800 to triple if it is invested at an annual intrest rate of 5.3%

A: P=$800 , R=5.3%

Q: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

A: Given: S the surface area of the cube, x the length of the cube and the length x of the cube…

Q: 2. How long will it take you to get ten times your money at 2% interest compounded continuously.

A:

Q: If 26 grams of radioactive waste reduces to 19.35 grams of radioactive waste after 1120 years, then…

A:

Q: Initially 100 millions of radioactive substance was present. After 6 hours the mass has decreased by…

A: Given query is to find the amount of radioactive substance after 24 hours.

Q: Suppose you invest $2000 at a rate of 3.25% continuously, what is the worth of the investment after…

A: Given that P = $2000  rate of Interest = 3.25% continuously, we have to find what is the worth of…

Q: A quantity with an initial value of 3600 grows continuously at a rate of 2.5% per decade. What is…

A:

Q: Suppose a small quantity of radon gas, which has a half-life of 3.8 days, is accidentally released…

A:

Q: A money market fund has a continuous flow of money at a rate of f(x)=1500x-170x2 for 10 years. Find…

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…

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.