Exam 4: Exponential Functions, Logarithms, and E

Find a number y such that .

Evaluate log₂(8xy) assuming that log₂x = 12.7 and log₂y = 7.1.

Suppose that the amount of the world's computer hard disk storage increases by a total of 300% over a 9-year period. What is the continuous growth rate for the amount of the world's hard disk storage?

For x = 9 and y = 4, evaluate each of the following. Round your answer to four decimal places. a) log(x + y) b) log x + log y

Evaluate . Round your answer to four decimal places.

Evaluate the indicated expression.

Evaluate . Round your answer to four decimal places.

Estimate the indicated value without using a calculator.

For x = 8 and y = 9, evaluate each of the following. Round your answers to four decimal places. A) B)

Suppose a colony of bacteria has a continuous growth rate of 18% per hour. By what percent will the colony have grown after 5 hours?

Without using a calculator or computer, determine which of the two numbers is larger.

Find a formula for estimating how long money takes to increase by a factor of 9 at R percent annual interest compounded continuously.

Suppose a savings account pays 5% interest per year, compounded twice per year. If the savings accounts starts with $700, how many years would it take for the savings account to exceed $4,000?

Suppose N is a positive integer such that log N $\approx$ 51.2. How many digits does N have?

Find the number t that makes As small as possible.

Evaluate (f g)(-1) for f(x) = 3^x and

Find the number of digits in the given number.

Estimate the indicated value without using a calculator.

Suppose a turbine at 25,000 RPM makes a noise of 147 decibels and at 30,000 RPM makes a noise of 163 decibels. What is the ratio of the sound intensity of the turbine at 30,000 RPM to the sound intensity at 25,000 RPM?

Suppose $3,200 is deposited in a bank CD account paying 6% interest per year, compounded 2 times per year. How much will be in the CD account at the end of 16 years? Round your answer to the nearest cent.