1. Radium decomposes in air at the rate proportional to the present amount. If initially

there are 20 grams, and after 10 years, 0.6% of the original decomposed:

a. Set a model that will predict the amount of radium at any time t.

b. When will the radium be half-life?

c. What is the amount remaining in 900 years?

2. Radium decomposes in air at the rate proportional to the amount present. It is found

out that in 25 years, 1.1% of a certain amount decomposed. Determine approximately

how long will it take:

a. For one-half of the original amount to decompose?

b. 20% of the amount to decompose

c. What percent of the amount will decompose in 50 years?

3. The population of the town grows at the rate proportional to the population present at

any time t. The initial population of 500 increases by 15% in 10 years. What will be the

population in 30 years?

4. A thermometer reading 10 degrees Celsius is brought in a room whose temperature is

18 degrees Celsius. One minute later, the thermometer reading is 14 degrees Celsius.

How long does it take until the reading becomes 16 degrees Celsius?

5. A metal is heated to a temperature of 500 degrees Celsius. It is then exposed to a

temperature of 38 degrees Celsius. After two minutes, the temperature of the metal

becomes 190 degrees Celsius. When will the temperature be 100 degrees Celsius? What

is the temperature after 4 minutes?

6. A thermometer is taken from an inside room to the outside, where the air temperature

is 5 degrees Fahrenheit. After one minute, the thermometer reads 55 degrees

Fahrenheit and after five minutes it reads 30 degrees Fahrenheit. What was the initial

temperature of the thermometer when inside the room?

7. A tank contains 200 litres of fluid in which 30 grams of salt or dissolved. Brine containing

1 gram of salt per litre is then pumped into the tank at the rate of four litres per minute

and the solution mixed well is pumped out of the same rate.

a. Find the number of grammes of salt in the tank at any time t in minutes.

b. Find the amount of salt in the tank after 5 minutes.

8. Brine containing 3 pounds per gallons of salt enters a large tank at the rate of two

gallons per minute and the mixture well stirred leaves at 1.5 gallons per minute. If the

tank contains initially 100 gallons of water, with four pounds of dissolved salt,

a. Find the amount of salt in data at any time t in minutes.

b. Find the amount of salt in the tank after 4 minutes.

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Radium decomposes in air at the rate proportional to the present amount. If initially there are 20 grams, and after 10 years, 0.6% of the original decomposed: a. Set a model that will predict the amount of radium at any time t. b. When will the radium be half-life? c. What is the amount remaining in 900 years?
Radium decomposes in air at the rate proportional to the amount present. It is found out that in 25 years, 1.1% of a certain amount decomposed. Determine approximately how long will it take: a. For one-half of the original amount to decompose? b. 20% of the amount to decompose c. What percent of the amount will decompose in 50 years?
The population of the town grows at the rate proportional to the population present at any time t. The initial population of 500 increases by 15% in 10 years. What will be the population in 30 years?
A thermometer reading 10 degrees Celsius is brought in a room whose temperature is 18 degrees Celsius. One minute later, the thermometer reading is 14 degrees Celsius. How long does it take until the reading becomes 16 degrees Celsius?
A metal is heated to a temperature of 500 degrees Celsius. It is then exposed to a temperature of 38 degrees Celsius. After two minutes, the temperature of the metal becomes 190 degrees Celsius. When will the temperature be 100 degrees Celsius? What is the temperature after 4 minutes?
A thermometer is taken from an inside room to the outside, where the air temperature is 5 degrees Fahrenheit. After one minute, the thermometer reads 55 degrees Fahrenheit and after five minutes it reads 30 degrees Fahrenheit. What was the initial temperature of the thermometer when inside the room?
A tank contains 200 litres of fluid in which 30 grams of salt or dissolved. Brine containing 1 gram of salt per litre is then pumped into the tank at the rate of four litres per minute and the solution mixed well is pumped out of the same rate. a. Find the number of grammes of salt in the tank at any time t in minutes. b. Find the amount of salt in the tank after 5 minutes.
Brine containing 3 pounds per gallons of salt enters a large tank at the rate of two gallons per minute and the mixture well stirred leaves at 1.5 gallons per minute. If the tank contains initially 100 gallons of water, with four pounds of dissolved salt, a. Find the amount of salt in data at any time t in minutes. b. Find the amount of salt in the tank after 4 minutes.

An inductance of L Henrys and a resistance of 10 ohms are connected in series with EMF of 100 volts. If the current is initially 0, and is equal to 9 amperes after one second, find L and find the current after 0.5 seconds.
An inductance of 1 Henry and a resistance of two ohms are connected in series with the constant emf of E volts. If the current is initially 0, and is equal to 10 A after five seconds, find E.
In a series RL circuit, L = 4 H, R = 100 ohms and E 200 volts. Find the values of current as a function of time. Assume that the initial current is zero. Find the current when t = 2 seconds.
Find the orthogonal trajectories of the family of parabolas y^2 = Cx.
Find the family of orthogonal trajectories of the circles x^2 + y^2 = C.
Find the orthogonal trajectory curve of the given curve: xy = C.
Find the orthogonal trajectory curve of all the lines passing through the origin.
A body of mass 4 kg falls (at rest) from a medium whose resisting force is numerically equal to 0.003V where V is the velocity in m/s. a. What is the velocity of the body at any time t? b. What is the velocity after 5 seconds?
A ball of mass of 2 kg is dropped from rest in a viscous fluid, the resistance of which is 0.001V Newton where V is the instantaneous velocity in m/s. What is the velocity and distance travelled by the ball after 4 seconds?
In a series RC circuit, R = 5 ohms, C = 0.01 Farad, and E = 100 Volts. When t = 0, i = 0. Find the charge at any time t.
A resistance of 10 ohms and C = 0.1 Farad is connected in series with a 12 V battery. Find the charge at any time and the charge and current 0.4 seconds after the switch is closed.
If the nominal interest rate is 3%, how much is 5,000 pesos worth in 10 years in a continuously compounded account?
The accumulated amount of 5,000 pesos is 20,000 pesos after 9 years. Calculate the interest rate if it is compounded continuously.
How long will it take a bank deposit to double if interest is compounded continuously at a constant rate of 4% per annum?

Differential Equations Applications: Exercises and Problems, Exams of Differential Equations

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