Exam 5: Exponential and Logarithmic Functions

Given ln x = 7.1; ln y = 8.2,find ln( )

A town of 1400 is growing at the rate of 8% per year.If this rate continues,what will the population of this town be in 20 years?

Assume the value of an RV depreciates by 22% every year. (a)Make a table of the factor of decrease in the value of the RV for 0 to 3 years.For each year,write an expression for the factor of decrease in the value of the RV 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 graph to guess when your RV will be worth a tenth of its original price. (e)Using the table you made,write a function for the depreciation as a function of years.Use a graphing calculator to graph your function.Use the graph to estimate when the RV will be worth a tenth of its original value.Compare this answer with the guess you made from your graph.

What power of 6 is 36?

Your friend started a savings plan with 3 pennies and each day she saved three times the amount she saved the previous day.Later you started a savings plan with 9 pennies and each day you saved 9 times the amount you saved the previous day.On the day that your friend had been saving for 8 less than 4 times as many days as you,you saved the same amount as your friend.How many days have you been saving?

Solve for x: log( + 4x + 104)= 2

Solve for x: y = 3

What power of is 36?

Solve for x: log(x + 1)- log(x - 2)= 1

Find x: (4x - 1)= 1

Find x: ln = x

If = 5,then x =

Solve: = 27

Assume the value of a computer depreciates by 30% every year. (a)Make a table of the factor of decrease in the value of the computer for 0 to 3 years.For each year,write an expression for the factor of decrease in the value of the computer 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 graph to guess when your computer will be worth a tenth of its original price. (e)Using the table you made,write a function for the depreciation as a function of years.Use a graphing calculator to graph your function.Use the graph to estimate when the computer will be worth a tenth of its original value.Compare this answer with the guess you made from your graph.

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

Assume the amount of paper being recycled quadruples every year. (a)Make a table of the factor of increase in the amount of paper being recycled at each year for 0 to 3 years.For each year,write an expression for the factor of increase as a power of some base. (b)What base did you use? How does that base relate to the problem? (c)Use your table to graph the factor of increase as a function of years. (d)Use your graph to estimate when the recycling will have grown by a factor of 50.

If ln x + ln 2 = ln 5,then x =

The population of a city is given by P = 1,000,000(1.0 where t is the number of years after 1987.The population in 1989 was

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.

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 7.5 on the Richter Scale,how many more times intense is it than a barely-felt earthquake?