Exam 4: Exponential Functions, Logarithms, and E

About how many years will it take for a sample of polonium-210 to have at most 7% as much polonium-210 as the original sample?

Evaluate Assuming that .

Evaluate log₅(x³y²) assuming that log₅x = 11.1 and log₅y = 6.1.

Suppose a colony of bacteria has doubled in 9 hours. What is the approximate percent per hour continuous growth rate of this colony of bacteria? Round your answer to the nearest whole percent.

Suppose a country's population increases by a total of 17% over a 7-year period. What is the continuous growth rate for this country? Round your answer to the nearest hundredth.

Find the inverse function.

Find a formula for (f g)(x) assuming that .

Suppose that you deposit into a savings account one cent on January 1, five cents on January 2, twenty five cents on January 3, and so on, quintupling the amount of your deposit each day. What is the first day that your daily deposit will exceed $10,000?

Find a number r such that Give the answer as a natural log.

About how many years will it take for a sample of plutonium-239 to have only as much plutonium-239 as the original sample?

A star with apparent magnitude 15 is brighter than a star with apparent magnitude 8.

Estimate the value of

Without using a calculator or computer, give a rough estimate of .

Assuming that f is a function defined by . A) Find the domain of f. B) Find the range of f. C) Find a formula for f ^-1.

The most intense recorded earthquake in the southeast states during a period of time had Richter magnitude 3.1. If an earthquake were to strike one of these states next year that was four times as intense as the current record, what would its Richter magnitude be?

A certain rodent colony of 80 individuals doubles its size every 11 months. How many months would it takes to this colony to reach the critical population of 10,000 individuals?

Suppose that r is a small positive number. Estimate the slope of the line containing the points and Give the answer as a power of e.

How much would an initial amount of $5,000, compounded continuously at 8% annual interest, become after 28 years?

Suppose that a colony of bacteria has a continuous growth rate of 33% per hour. How many hours does it take the colony to triple in size? Round your answer to the nearest hundredth.

Find a number y such that ln y = 3.