Exam 5: Exponential and Logarithmic Functions

The number of years it takes for an amount which is invested at an annual rate of p and compounded continuously to become m times as large is given by t = .How long does it take an investment to quadruple if it is invested at an annual rate of 7% and compounded continuously?

Assume the value of a sailboat depreciates by every year. (a)Make a table of the factor of decrease in the value of the sailboat for 0 to 3 years.For each year,write an expression for the factor of decrease in the value of the sailboat as a power of some base. (b)What base did you use? How does the base relate to the problem? (c)Use your table to graph the factor of decrease as a function of years. (d)Use your table to guess when your boat will be worth 25% as much as its original price.

If the yeast has been decreasing by 80% hourly and the current amount is of the amount first measured,then the situation can be represented by = .Represent this equation in logarithmic form.What does t represent?

Consider h(x)= 2ln(x)- 3 (a)Graph h(x) (b)Find the domain of h(x)

Solve for x: = 20

If log 3 = 0.4771,then log 0.3 =

If log 2 = 0.3010 and log 3 = 0.4771,then log 18 =

Suppose $2000 is invested at 6.5% compounded monthly. (a)Find the value of the investment after 5 years. (b)Find the value of the interest which was earned over the first 5 years.

Assume ln x = 2; ln y = 7.Find ln( ).

log =

Evaluate and simplify: 1 + 2

Simplify:

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

Of the following the best approximation of e is

Assume that log 4 = 0.6021.Determine the value of log .

Find x and express your answer in terms of common logarithms: = 4

Suppose $2000 is invested at 6.5% compounded quarterly. (a)Find the value of the investment after 5 years. (b)Find the value of the interest which was earned over the first 5 years.

Solve for x: - 2 ∙ - 3 = 0

Assume your savings consist of a $5000 investment which is guaranteed to increase by 7% every year and $800 cash in a safe at your home. (a)Make a table of the value of your investment at 0 to 3 years. (b)Make a table of the value of total savings at 0 to 3 years. (c)How could you use the graph of (a)to make a graph of (b)? Verify your answer using a graphing calculator.

What is the sum of the Richter Scale measurement of an earthquake which is 250,000 times the intensity of a zero-level earthquake and an earthquake with intensity twice the intensity of a zero-level earthquake? Write as an expression involving logarithms.Simplify by combining logarithms and then use a calculator to evaluate.