Exam 4: Exponential Functions, Logarithms, and E

How much would an initial amount of $4,000, compounded continuously at 5% annual interest, become after 10 years?

Estimate the slope of the line containing the points (5, ln 5) and

Estimate the indicated value without using a calculator.

Evaluate . Round your answer to four decimal places.

Find a number y such that

Find all numbers x that satisfy the given equation.

For x = 21 and y = 2.4, evaluate each of the following. Round your answer to four decimal places. a) b)

Find a number t such that . Round your answer to four decimal places.

Suppose a bank wants to advertise that $2,000 deposited in its savings account will grow to $2060 in one year. This bank compounds interest 4 times per year. What annual interest rate must the bank pay? Round your answer to one decimal place.

About how many years does it take for $200 to become $800 when compounded continuously at 5% per year?

The earthquake that occurred in Chile in 1960 was 1000 times more intense than the one that occurred in Wyoming in 1959, which had a Richter magnitude of 6.5. Determine Chile's earthquake magnitude.

Suppose you normally speak at 65 decibels and your dog barks at 75 decibels. How many times louder does your pet barks seem as compared to your normal speech?

Find all numbers x that satisfy the given equation. Ln(x + 6) + ln(x - 6) = 4

How many times brighter is a star with apparent magnitude 6 than a star with apparent magnitude 21?

Suppose one bank account pays 8% annual interest compounded once per year, and a second bank account pays 8% annual interest compounded continuously. If both bank accounts start with the same initial amount, how many years will it take for the second bank account to contain double the amount of the first bank account?

How many years does it take for money to triple when compounded continuously at 9% per year? Round your answer to the nearest year.

Suppose the fire alarm of a building makes a noise of 86 decibels and the emergency system speakers work at 68 decibels. How many times louder does the fire alarm seem as compared to the speakers? Round your answer to the nearest tenth.

Estimate the value of . Give the answer as a power of e.

For x = 6 and y = 7, evaluate each of the following. Round your answers to four decimal places. A) ln(x + y) B) ln x + ln y

Find a formula for Assuming that f(x) = ln x and