Because of an insufficient oxygen supply, the trout population in a lake is dying. The population's rate of change can be modeled by dP/dt= -130e-t/20 where t is the time in days. When t = 0, the population is 2,600. (a) Find a model for the population.     (b) What is the population of fish after 13 days? (Round your answer to the nearest integer.)   (c) How long (in days) will it take for the entire trout population to die? (Assume the entire population has died off when the population is less than one. Round your answer to one decimal place.)

Q: Water is drained from a swimming pool at a rate given by |(-0.2)t R(t) = 100e' gallons per hour. If…

A: Solution : We have given the rate of water drain form a swimming pool is R(t) = 100e(-0.2)t…

Q: According to a particular model for predicting the height of preschool children, the rate of growth…

A: Given  Rt=25.907e-0.983t+5.12

Q: A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its…

A: Refer to the figure shown below: [Note that we have to consider the depth of 5 ft to solve the…

Q: When polluted water begins to flow into an unpolluted pond, the concentration of pollutant, c, in…

A:

Q: 1. A 25 feet long ladder is leaning against a wall and sliding toward the floor. If the foot of the…

A:

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: In some chemical reactions, the rate at which the amount of a substance changes with time is…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Alice measures a radioactive sample at 1400 counts/minute on a Geiger counter. If the radioactive…

A: Given: Initial value, R0=1400 counts/min Ending value, R = 1000 counts/min Time that has passed, t =…

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A: To find the rate of change of the carbon monoxide levels per population when t=2

Q: The population of a town grows at a rate proportional to the population present at time t. The…

A: Y(t)=Population in year tY(0)=700Y(15)=700+20%700=700+140=840

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

A:

Q: In the equation, x² +y² = 45, what is the value of the rate of change in y with respect to time t…

A:

Q: The upper end of the ladder 5 m long leans against a vertical wall. Suppose the foot of the ladder…

A:

Q: An object is moving so that it's velocity after t hours is v(t)=te^-t^2 mph. How far does it travel…

A: Hey the equation of velocity that you have written is v(t)=t·e-t2mph following is the solution to…

Q: Suppose that electricity isdraining from a capacitor at a rate that is proportional to the voltageV…

A: Given equation in the question is: Integrating both sides: We have, at t = t0, V  = V0 =>ln(V0)…

Q: A chemical flows into a storage tank at a rate of (180 + 3t) liters per minute, where t is the time…

A:

Q: If we put a cool object into a preheated oven, Newton's law of heating tells us that the difference…

A: Given: A potato initially has a temperature of 75 degrees and the oven is preheated to 375 degrees.…

Q: Hello, I need help answering the following question. This is in a lesson regarding antiderivatives…

A: Given thatThe velocity of the package initially at the time of the drop = 12 ft/sec Initial height…

Q: | Suppose that electricity is draining from a capacitor at a rate proportional to the voltage V…

A: The given differential equation is dVdt=-140V, where V is the voltage and t is the time in seconds.…

Q: One model for the way diseases die out when properly treated assumes that the rate dy/dt at which…

A:

Q: On the moon, the acceleration of a free-falling object is a(t) = −1.6 meters per second per second.…

A:

Q: 1. A balloon leaves the ground 18m from an observer and rises vertically at 1.25 m/s. How fast is…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Given,           Because of job outsourcing, a town predicts that its public school population will…

Q: 4. A culture initially has No number of bacteria. After one hour the number of bacteria is measured…

A: Topic = Differential equation

Q: udent is walk

A: Here it is given that,  A student is walking towards the foot of a flagpole 20 meters high at the…

Q: A child flies a kite at 90ft. The wind is carrying the kite horizontally away from the child at a…

A:

Q: 18. A light is on the top of a 4-meter tall pole and a 1.5-meter tall person is walking away from…

A:

Q: A culture initially has No number of bacteria. At t =1hours the number of bacteria is measured to be…

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: A rocket rising from the ground has a velocity of v(t)=2,000 te-t/180 ft/s, after t seconds. How far…

A: Given thatThe velocity of the rocket rising from the ground is

Q: 4. A culture initially has No number of bacteria. After one hour the number of bacteria is measured…

A: Given:- Rate of growth dNdt=kN N0= initial number of bacteria

Q: The air in a small room 12 ft by 8 ft by 8 ft is 5% carbon monoxide. Starting at t = 0, fresh air…

A: Let v(t) be the volume of CO in the room at time t, and let V be the total volume of the room.The…

Q: A ladder 13 ft long is leaning against a wall. The bottom of the ladder is being pulled away from…

A:

Q: Because of heavy rainfall, the water level in a reservoir is rising at a rate of g(t) feet per hour,…

A: Given problem :- Because of heavy rainfall, the water level in a reservoir is rising at a rate of…

Q: 10. Romeo is walking towards North at a rate of 4m/s. Ten seconds after, Juliet walks towards East…

A:

Q: The population of a town grows at a rate proportional to the population present at time t. 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: A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec. How…

A: Given; A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec.

Q: The population of a town grows at a rate proportional to the population present at time t. The…

A:

Q: According to a particular model for predicting the height of preschool children, the rate of growth…

A: Given,Rate of growth of a child, R(t) = 24.348 e-0.993t+ 6.41  cm/yr    t∈ (0.25,6)Height of child…

Q: A balloon is released from the ground 100 m from an observer. The balloon rises directly upward at…

A:

Q: The number of cell phone subscribers in a certain country in the early 2000s was projected to follow…

A:

Q: A cement mixer is pouring concrete in a conical pile. At the time when the height and base radius of…

A:

Q: Suppose that electricity is draining from a capacitor at a rate that is proportional to the volt-age…

A: Separate the variables.

Q: A brine solution of salt flows at a constant rate of 3 L/min into a large tank that initially held…

A:

Q: The population of a town grows at a rate proportional to the population present at time t. The…

A: according to questiondPdt=kP1PdP=kdtintegrate∫1PdP=∫kdtlogP=kt+C    where C is any constanttaking…

Q: The population of a town grows with a ratio proportional to the population at time "T". The initial…

A:

Q: According to a particular model for predicting the height of preschool children, the rate of growth…

A: Rt=25.395e-0.984t+5.42   14≤t≤6 a). To find the height, integrate the rate of growth function with…

Q: A 14-foot ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate…

A:

Q: If oil leaks from a tank at a rate of  r(t) gallons per minute attime t , what does ∫0120 r(t) dt…

A: Oil leaks from a tank at a rate of  r(t) gallons per minute at time t.

Q: 13-foot ladder is leaning against a wall. If we pull the ladder away from the wall at a rate of 4…

A:

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.