Exam 4: Exponential Functions, Logarithms, and E

Evaluate the indicated expression.

Suppose one bank account pays 9% annual interest compounded once per year, and a second bank account pays 10% 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 50% more than the first bank account?

Find the number of digits in the given number.

Evaluate . Round your answer to four decimal places.

Find a formula for the inverse function of the indicated function f.

Assuming that f is a function defined by f(x) = 6 - 9ln(x). A) Find the domain of f. B) Find the range of f. C) Find a formula for f ^-1.

Any bacteria population can have exponential growth indefinitely.

Find all numbers x that satisfy the equation . Round your answer to two decimal places.

For x = 9 and y = 8, evaluate each of the following. Round your answer to four decimal places. A) log(x^y) b) (log x)^y

Find a number x such that

Two stars with apparent magnitude 0.01 and 0.23 have been observed. How many times brighter is one of these stars than the other one. Round your answer to the nearest tenth.

Find all numbers x such that e^2x + e^x = 20. Round the answer to 4 decimal places.

Suppose log a = 106.68 and log b = 109.68. Evaluate b/a.

Evaluate the indicated expression.

How much would you need to deposit in a bank account paying 4% annual interest compounded continuously so that at the end of 2 years you would have $10,000?

Find a number x such that .

Find all numbers x such that ln(x² - 3) = 4.

How much would you need to deposit in a bank account paying 4% annual interest compounded continuously so that at the end of 19 years you would have $20,000?

Find all such numbers x such that $log{\_}_2|x| = (3x + 4) = 4$ holds.

Find all numbers x that satisfy the equation .