Exam 5: Exponential and Logarithmic Functions

Your friend started a savings plan with 2 pennies and each day he doubled the amount saved.Later you started a savings plan with 4 pennies and each day you quadrupled the amount saved.Your friend has been saving for 6 less than 3 times as many days as you.In two days you will put the same amount in savings as your friend.How many days have you been saving?

What is the sum of the Richter Scale measurement of an earthquake which is 37,000 times the intensity of a zero-level earthquake and an earthquake with intensity 1000 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.

Evaluate and simplify: 6

The multiplicative increase m of an investment which is invested at an annual rate of p and compounded continuously for a time t is given by m= .If your annual rate is 6.75%,how many years will it take to double your investment?

The multiplicative decrease in purchasing power P after t years of inflation at 3% can be modeled by Graph the decrease in purchasing power as a function of t years.

=

Express 2 ln 3 - ln 4 as a single logarithm.

Suppose $2000 is invested at 6.5% compounded daily (exclude extra day for leap year). (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.

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

A trust fund is being set up by a single payment so that at the end of 30 years there will be $20,000 in the fund.If the interest rate is 8% compounded quarterly,how much money should be paid initially into the trust fund?

Find x: (4x -3)= 2

Write the following in terms of ln x,ln(x - 3),and ln(x + 1):

Find x if 7 = 1

Find x: (x + 4)= 3

The value of an investment of $3000 earning 7.25% compounded yearly is given by A = 3000(1.072 ,where t is the number of years it has been invested.If the amount of your investment is now $10,000,how long has it been invested?

Write the following in terms of ln x,ln(x - 3),and ln(x + 1): ln

Evaluate and simplify: ln

The demand function for a product is p = 60 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 $41.60?

Changing (4x)to natural logarithms gives

Solve for x: = 2