Exam 4: Exponential and Logarithmic Functions

Solve the problem. -An earthquake was recorded which was 125,893 times more powerful than a reference level zero earthquake. What is the magnitude of this earthquake on the Richter scale? Intensity on the Richter scale is

Rewrite the expression as a single logarithm. -

Find the value of the logarithmic function. -ln(1)

Use a graphing calculator to solve the equation. Round to two decimal places. -

Solve the equation. -

Solve the problem. When needed, use 365 days per year and 30 days per month. -An initial investment of $1000 is appreciated for 7 years in an account that earns 11% interest, compounded annually. Find the amount of money in the account at the end of the period.

Graph the function. -

Solve the problem. -The number of dislocated electric impulses per cubic inch in a transformer when lightning strikes is given by , where x is the time in milliseconds of the lightning strike. Find the number of dislocated impulses at x = 0 and x = 3.

Graph the function. -

Rewrite the expression as a sum or difference of logarithms or multiples of logarithms. -

Solve the problem. -The average salary for Major League Baseball players has been increasing exponentially since 1980. The average salary S can be modeled by the exponential equation where t is the number of years since 1980. Use the model to predict the year when the average salary will be $10 million more than it was in the year 2000?

Graph the function. -

Solve the problem. -Ben Franklin bequeathed $4000.00 to the city of Boston in 1790. Assuming the fund grew to $9 million in 200 years, find the interest rate compounded continuously that would yield this total value. Round to the nearest Tenth when necessary.

Solve the equation. -

Solve the problem. -A certain radioactive isotope has a half-life of approximately 1250 years. How many years to the nearest year would be required for a given amount of this isotope to decay to 20% of that amount?

Rewrite the expression as a sum or difference of logarithms or multiples of logarithms. -

Simplify the expression. -

Find the inverse of the function. -f(x) = log(x + 2)

Solve the equation. If necessary, round to thousandths. -

Use a calculator and the base-change formula to find the logarithm to four decimal places. -