Exam 5: Exponential and Logarithmic Functions

If = 7,then x =

Solve for x: ( = 129.3

The number of years it takes for an amount which is invested at an annual rate of 7% and compounded continuously to become m times as large is a function of the enlargement factor given t(m)= .Use a graphics calculator to find how many times larger (to the nearest whole number increment)the investment will be in 10,20,30,and 40 years.

Evaluate and simplify: log (0.1)

Find x: 36 = x

Suppose a garbage company has found that garbage per family has decreased by 10% every year since the first year they started a curb-side recycling program.Graph each year as a function of the multiplicative decrease in garbage since the first year of the curb-side recycling program.Label the graph with the name of the function.

Simplify:

Evaluate and simplify: ln

Solve for x: (x - 4)+ 3 = x

Express 64 = 3 in exponential form.

Solve for x: = 10

Writing [ln x - 2(ln y + 2 ln z)] as a single logarithm gives

Hannah wants to use her graphing calculator to check this sketch of y = x but her calculator does not make calculations.Find two equations she could use.Use a graphing calculator to confirm that the two equations are equivalent.

Write x in terms of natural logarithms.

Find x: = x

Graph y = f(x)= .

The population of India was 651 million in 1980 and has been growing at a rate of 2% per year.The population t years later is approximated by N(t)= .Estimate the population in India in the year 2010.

Find x: log x = 3

Evaluate and simplify: log 100

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 2,000,000 times the intensity of a zero-level earthquake.