Exam 5: Exponential and Logarithmic Functions

Write the following in terms of ln x and ln(x + 1):

Suppose that the number of patients admitted into a hospital emergency room during a certain hour of the day has a Poisson distribution with mean 3.Find the probability that during that hour there will be exactly two emergency patients.Assume that = 0.05.

How much more on the Richter Scale is an earthquake with intensity 300,000 times the intensity of a zero-level earthquake than an earthquake with intensity 150,000 times the intensity of a zero-level earthquake? Write as an expression involving logarithms.Simplify by combining logarithms and then use a calculator to evaluate.

How long will it take for $100 to amount to $200 at an interest rate of 10% compounded annually? Give your answer to 2 decimal places.

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

Find x: log 100,000 = x

Express 2 log(x)- 3 log(x + 7)as a single logarithm.

Solve for x: =

Find x: = x

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 than the earthquake is than the reference earthquake.If an earthquake measured 4.2 on the Richter Scale,how many more times intense is it than a zero-level earthquake?

Graph h(x)= - 1

If (x + 3)= -2,then x =

If the pH of a substance is 9.2,then the concentration of hydrogen ions h in gram-atoms per liter can be represented by 9.2 = log .Represent this equation in exponential form.

Graph f(x)= x

log 0.001 =

A graphical look at Bacteria Growth: If 100 bacteria are present at the start,the number of bacteria in a culture which changes by constant factor f every hour is given by N(t)= 100( ).Use a graphing calculator to graph this function for various values of f where f > 0.Describe how the graphs where 0 < f < 1 differ from the graphs where f > 1.How does the number of bacteria change when 0 < f < 1? How does the number of bacteria change when f > 1? Describe the graph where How does the number of bacteria change when f = 1?

If (x + 6)= 2 - X,then x =

Suppose a computer decreases in value by 50% every year.Graph the number of years it is owned as a function of the multiplicative decrease in its original value.Label the graph with the name of the function.

The demand function for a product is p = 180 where q is the number of units and p is the price of one unit.At what price will the demand be 15 units? How many units will be demanded if the price is $24.91?

If an earthquake is times as intense as a zero-level earthquake,what is its measurement on the Richter Scale? Write as logarithmic expression and simplify.