Exam 7: Exponential Functions

Bob's retirement account pays about $120,000 per year, continuously for 20 years. Find the present value of the income stream if the interest rate is 5.5%.

A mug of hot chocolate with initial temperature C is placed on a table in a room held at a constant temperature. After 20 min, the temperature of the hot chocolate is C. After another 20 min, the temperature of the hot chocolate is C. What is the temperature of the room?

Compute the following limits: A) B)

A 3-kg object is dropped from a tall building. After 1 s, the object has a velocity of m/s. What is the object's terminal velocity?

The population in an ant colony doubles every 3 months. Assuming exponential growth, how many years does it take the population to increase five fold?

Find the slope of the function at .

Let . Use logarithmic differentiation to calculate .

Find the limits using L'Hopital's Rule: A) B)

Find the slope of the function at . To find use the equality or use a calculator.

Calculate the definite integrals: A) B)

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

Apply L'Hopital's Rule to evaluate the limit A) B) C)

Let be the inverse of . Use the geometric relation between the graphs of inverse functions to compute the integral .

Consider the Gompertz differential equation . Define the function by . The differential equation for is,

How much would a 20-year-old have to invest today in order to have $1 million 30 years from now if the interest is compounded continuously at an annual rate of 6.4%?

Evaluate the integral

Solve

Evaluate the integrals: A) B) C)

A mug of hot chocolate with initial temperature C is in a room held at C. After 30 min, the temperature of the hot chocolate is C. What is the temperature of the hot chocolate after another 10 min?

A glass of cold water with initial temperature C is placed in a room held at a constant temperature. After 1 h, the water temperature is C. After another 2 h, the water temperature is C. What is the temperature of the room?