Exam 5: Exponential and Logarithmic Functions

Assume that log 5 = 0.6690.Determine the value of log 500.

Assume that log 3 = 0.4771.Determine the value of log 27.

Use the change base formula and your graphing calculator to graph f(x)= -3 (x + 4)+ 1

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

Solve for x: ln(x + 3)= ln(2x)

Graph y = f(x)= .

Write the following in terms of ln(x + 2)and ln(x + 4): ln

Graph g(x)=

Suppose $2000 is invested at 6.5% compounded annually. (a)Find the value of the investment after 10 years. (b)Find the value of the interest which was earned over the first 10 years.

Find x: x = 3

The number of yearly visitors to a resort has been shrinking at the rate of 6%.Currently the resort gets 120,000 tourists each year. (a)If this rate continues,how many tourists will they get in 15 years? (b)Use a graphing calculator to predict the number of years until the number of tourists will be less than 20,000.

A company is downsizing and expects the number of employees to shrink at the rate of 3% per month.Currently the company employs 30,000 people. (a)How many people are expected to be employed with this company in 1 year? (b)Use a graphing calculator to predict the number of months until the number of employees will be half its current size.

Evaluate and simplify: ln + ln 1

If $400 is invested for 2 years at 6% compounded semiannually,find (a)the compound amount and (b)the compound interest.

Solve for x: x = 5

The number of bacteria in a culture is growing by 40% every hour.Currently the culture has 500 bacteria.Make a table of values for the number of bacteria present each hour for 0 to 4 hours.For each hour write an expression for the number of bacteria as a product of 500 and a power of 1.4.Use the expressions to make an entry in your table for the number of bacteria after t hours.Write a function N for the number of bacteria after t hours.

Express 2(ln 4 + ln 3 - 3 ln 2)as a single logarithm.

Solve for x: = 4

Sean and Carley have bacterial infections.Sean was given medicine which reduces the number of bacteria hourly by 20%.5 hours later Carley began the same treatment. (a)If y = 0. represents the multiplicative decrease of bacteria for Carley,write an equation using the same reference that represents the multiplicative decrease in the bacteria in Sean. (b)If a doctor had a graph of the multiplicative decrease of bacteria for Carley,how could she use it to graph the multiplicative decrease of the bacteria in Sean? Verify your answer using a graphics calculator.

Solve for x: ln = x