Exam 7: Exponential Functions

From the top of a tall building, a 2-kg object is thrown vertically downward. One second after being thrown, the object has a velocity of m/s. If the coefficient of air resistance is kg/s, what was the initial velocity of the object?

Calculate where is the inverse of : A) B)

Find the domain on which is one-to-one and a formula for the inverse of .

From the top of a tall building, a 5-kg object is thrown vertically downward. One second after it is thrown, the object has a velocity of m/s. Two seconds after it is thrown, the object has a velocity of m/s. What was the initial velocity of the object?

Calculate the integral in terms of inverse hyperbolic functions

Find an equation of the tangent line to the graph of the function for .

Let . Calculate .

Evaluate the limits using L'Hopital's Rule

By Newton's Law of Cooling, an object in air cools down at a rate proportional to the difference between the object's temperature and the air temperature. When the air temperature is C, it takes 10 min for the object to cool down from C to C. The temperature of the object decreases from C to C during:

How long will it take for your money to double when it is invested at an annual rate of and compounded yearly? How long will it take for your money to double at an annual rate of ?

is deposited into an account earning interest at an annual rate of . Find the value of the account after one year if A) it is compounded twice a year. B) it is compounded monthly. C) it is compounded weekly (52 weeks a year) D) it is compounded daily (365 days a year) E) it is compounded continuously. Does the method of compounding have much effect on the final value?

Use the definition of the derivative at to find if .

Evaluate the limits using L'Hopital's Rule A) B) C)

From the top of a tall building, a 1-kg object is thrown vertically downward. One second after being thrown, the object has a velocity of m/s. Two seconds after being thrown, the object has a velocity of m/s. What is the coefficient of air resistance ?

Calculate the definite integrals: A) B)

Let with domain . Find

A mug of hot chocolate with initial temperature is placed on a table in a room held at C. After 15 min, the temperature of the hot chocolate is C. After an additional 30 min, the temperature of the hot chocolate is C. What was the initial temperature ?

The population of a country was in 1980, whereas in 1990 it was A) Find the population in B) Determine the population's doubling time. Assume that the rate of growth is proportional to the population.

The decay constant of a 15-kg isotope is 0.137 (years) . Find the half-life of the isotope.

A population is modeled by a function . Initially, the population counts 1000. The rate of change of the population is proportional to . Find the population at time years given that the doubling time is 8 years.