Exam 10: Geometric Series

Consider the sum . A. Calculate the partial sum . Round to 4 decimal places. B. Calculate the infinite sum S. Round to 4 decimal places.

Find the sum of . If it does not exist, enter "DNE".

Is a geometric series?

A radioactive isotope is released into the air as an industrial by-product. This isotope is not very stable due to radioactive decay. Two-thirds of the original radioactive material loses its radioactivity after each month. If 11 grams of this isotope are released into the atmosphere at the end of the first and every subsequent month, how many grams radioactive material are in the atmosphere at the end of the twelfth month? Round to 1 decimal place.

Find the sum of . If it does not exist, enter "DNE".

Suppose the government spends $3 million on highways. Some of this money is earned by the highway workers who in turn spend $1,500,000 on food, travel, and entertainment. This causes $750,000 to be spent by the workers in the food, travel, and entertainment industries. This $750,000 causes another $375,000 to be spent; the $375,000 causes another $187,500 to be spent, and so on. (Notice that each expenditure is half the previous one.) Assuming that this process continues forever, how many million dollars in total spending is generated by the original $3 million expenditure?

An account earns 5% interest per year, compounded annually. Suppose payments of $6000 each are to be made once a year from the account for 10 years, starting now. How much must be deposited now to cover these payments? Round to the nearest dollar.

A farmer sells 10,000 pounds of potatoes per year. The current selling price is $0.20 per pound, but this price goes up 4% each year because of inflation. Predict the farmer's total earnings from potato sales over the next 10 years. Round to the nearest dollar.

Find the sum of the first 8 terms of the series . Round to 2 decimal places.

Find the market stabilization point if 5000 new units are manufactured each year and 15% of the total number of units in use fail each year.

A school librarian estimates that 2% of the library's books are either lost or damaged each year and need to be pulled from the shelves. There are currently 250,000 books in circulation, and the library adds 6,000 books each year. Is the library currently gaining or losing books?

A yearly deposit of $10,000 is made into an account that pays 4.7% interest per year, compounded annually. What is the balance right after the 8^th deposit? Round to the nearest cent.

Use the fact that and your knowledge of geometric series to find a fraction equal to

Find the sum of . If it does not exist, enter "DNE".

A ball is dropped from a height of 10 feet and bounces. Each bounce is 2/3 the height of the bounce before. Find an expression for the height to which the ball rises after it hits the floor for the n^th time, and use it to find the total vertical distance the ball has traveled when it hits the floor for the 4^th time. Round to 2 decimal places.

Which of the following are geometric series? Select all correct answers.

A person takes 200 milligrams of a pain killer every 4 hours. If the pain killer has a half life of 3 hours, how many milligrams of the drug are in the body in the long run, right after each dose? Round to 1 decimal place.

Find the sum of the series . Round to 2 decimal places.

Twice a day, a patient takes a 25 milligrams tablet of a drug. At the end of a 12 hour period, 25% of the drug remains in the body. How many milligrams of the drug remain in the body at the steady state level, right after taking a tablet?

Is the following a geometric series? Answer "Yes" or "No".