Exam 5: Exponential and Logarithmic Functions

Find the second derivative of the function.

A condominium complex was purchased by a group of private investors for $1.8 million and sold 6 year(s) later for $3.5 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth. __________%

Evaluate the expression. = __________

Find the interest rate needed for an investment of $4,000 to grow to an amount of $8,500 in 2 year(s) if interest is compounded monthly. Round your answer to the nearest hundredth. __________%

Solve the equation for x.

Given that a quantity Q(t) exhibiting exponential decay is described by the function where t is measured in years. What is the decay constant? What quantity is present initially? Complete the table of values. Round your answer to the nearest integer.

The concentration of a drug in an organ at any time t (in seconds) is given by where is measured in grams/cubic centimeter . Please round the answer to two decimal places. How long would it take for the concentration of the drug in the organ to reach ? __________ sec How long would it take for the concentration of the drug in the organ to reach ? __________ sec

Wood deposits recovered from an archeological site contain 22% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Round your answer to the nearest year. Hint: the decay constant k for carbon 14 is equal to 0.00012. __________ years

The concentration of a drug in an organ at any time t (in seconds) is given by where C(t) is measured in milligrams/cubic centimeter . What is the initial concentration of the drug in the organ? __________ What is the concentration to four decimal places of the drug in the organ after 10 sec? __________ What is the concentration to four decimal places of the drug in the organ after 30 sec? __________ What will be the concentration of the drug in the long run? __________

Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent. P = $180,000, r = 8%, t = 4, compounded daily

Find an equation of the tangent line to the graph of at its inflection point.

Find the derivative of the function.

Use the laws of logarithms to simplify the expression.

Use logarithms to solve the equation for t. Please round the answer to four decimal places. __________

Find the derivative of the function.

Use logarithms to solve the equation for t. Round your answer to four decimal places.

Sketch the graphs of the functions on the same axes.

Online retail sales stood at $22.7 billion for 2000. For the next 2 years, they grew by 32.4% and 27.4% per year, respectively. For the next 6 years, online retail sales are projected to grow at 30.5%, 19.6%, 24.2%, 13.4%, 17.4%, and 10.1% per year, respectively. What are the projected online sales for 2008? Round your answer to the nearest tenth. $__________ billion

Find the derivative of the function.

If the temperature is constant, then the atmospheric pressure P (in pounds/square inch) varies with the altitude above sea level h in accordance with the law where is the atmospheric pressure at sea level and k is a constant. If the atmospheric pressure is at sea level and at 5,000 ft, how fast is the atmospheric pressure changing with respect to altitude at an altitude of 15,000 ft? Give the answer to four decimal places.