Exam 5: Exponential and Logarithmic Functions

Assume an investment is guaranteed to triple every decade. (a)Make a table of the factor of increase in the investment at each decade for 0 to 3 decades.For each decade,write an expression for the factor of increase as a power of some base. (b)What base did you use? How does that base relate to the problem? (c)Use your table to graph the factor of increase as a function of decades. (d)Use your graph to estimate when the investment will have grown by a factor of 15.

Given ln x = 7.1; ln y = 8.2,find ln .

If $2000 is invested for 3 years at 8% compounded quarterly,find (a)the compound amount and (b)the compound interest.

The population of a city is given by P = 100,000(1.0 where t is the number of years after 1988.Find the population in (a)1988 (b)1989 (c)1990.

The work done by 1 kilogram sample of nitrogen as its volume changes from an initial value to a final value of during a constant temperature process is given by W = 3.2 × ln .If such a sample expands from a volume of 3 liters to a volume of 5 liters,determine the work done by the gas.

For the function f(x)= , (a)what is the domain of f? (b)What is the range of f?

Write the following in terms of ln(x + 2)and ln(x + 4): ln

Assume that log 3 = 0.4771 and log 4 = 0.6021.Determine the value of log 36.

R = log gives the Richter Scale measurement of an earthquake with intensity I where is the intensity of a zero-level earthquake.Make a graph which converts the intensity of the earthquake as compared to a zero-level earthquake to the Richter Scale measurement.

The above graph is best represented by

An earthquake measuring 5.8 on the Richter scale can be represented by where I is the intensity of the earthquake and is the intensity of a zero-level earthquake.Represent this equation in exponential form.

The magnitude (Richter Scale)of an earthquake is given by R = log where I is the intensity of the earthquake and is the intensity of a zero-level reference earthquake. represents how many times greater the earthquake is than the reference earthquake.Find the magnitude of an earthquake that is 200 times the intensity of a zero-level earthquake.

Suppose $5000 is deposited in a savings account that earns 10% compounded semiannually.What is the value of the account at the end of 6 years? Assume no other deposits or withdrawals.

ln =

Initially,three are 50 milligrams of a radioactive substance.The substance decays according to the equation N = 50 ,where N is the number of milligrams present after t hours.The number of hours it takes for 10 milligrams to remain is

ln e - ln 1 =

Assume that log 6 = 0.7782.Determine the value of log 36.

If ln 2 = 0.7 and ln 5 = 1.6,find 5.