To stimulate the economy, the government gives a tax rebate totaling 5 billion dollars

In Problems 18, find the sum, if it exists. 2 + 22 + 23 + + 210

In Problems 18, find the sum, if it exists. 20 + 20(1.4) + 20(1.4)2 + + 20(1.4)8

In Problems 18, find the sum, if it exists. 1000+1000(1.08)+1000(1.08)2 +1000(1.08)3 +

In Problems 18, find the sum, if it exists. 500 + 500(0.6) + 500(0.6)2 + +500(0.6)15

In Problems 18, find the sum, if it exists. 30 + 30(0.85) + 30(0.85)2 + 30(0.85)3 +

In Problems 18, find the sum, if it exists. 25 + 25(0.2) + 25(0.2)2 + 25(0.2)3 +

In Problems 18, find the sum, if it exists. 1 + 1 2 + 1 22 + + 1 28

In Problems 18, find the sum, if it exists. 1 + 1 3 + 1 32 + 1 33 +

Around January 1, 1993, Barbra Streisand signed a contract with Sony Corporation for $2 million a year for 10 years. Suppose the first payment was made on the day of signing and that all other payments were made on the first day of the year. Suppose also that all payments were made into a bank account earning 4% a year, compounded annually. (a) How much money was in the account (i) On the night of December 31, 1999? (ii) On the day the last payment was made? (b) What was the present value of the contract on the day it was signed?

A drug is given in daily doses of 100 mg. After 24 hours, 82% of the previous days dose remains in the body. What is the long-run quantity of drug in the body, right after and right before a dose is given?

A used car costs $15,000. The repair contract costs $500 at the end of the first year and increases by 20% at the end of each subsequent year. Find the total cost of owning the car for ten years. Include the payment at the end of the tenth year.

A deposit of $100,000 is made into an account paying 8% interest per year, compounded annually. Annual payments of $10,000 each, starting right after the deposit, are made out of the account. How many payments can be made before the account runs out of money?

This problem shows how to estimate the cumulative effect of a tax cut on a countrys economy. Suppose the government proposes a tax cut totaling $100 million.We assume that all the people who have extra money spend 80% of it and save 20%. Thus, of the extra income generated by the tax cut, $100(0.8) million = $80 million is spent and becomes extra income to someone else. These people also spend 80% of their additional income, or $80(0.8) million, and so on. Calculate the total additional spending created by such a tax cut.

To stimulate the economy, the government gives a tax rebate totaling 5 billion dollars. Find the total additional spending resulting from this tax rebate if everyone who receives money spends (a) 80% of it (b) 90% of it

A government gives a tax rebate ofN dollars to stimulate the economy. Everyone who receives money spends a fixed fraction, k, of themoney received,with 0 < k < 1. (a) Find a formula (in terms of N and k) for the total additional spending resulting from the tax rebate. (b) If k = 0.85, what is the total additional spending as a multiple of the size, N, of the tax rebate?

Before World War I, the British government issued what are called consols, which pay the owner or his heirs a fixed amount of money every year forever. (Cartoonists of the time described aristocrats living off such payments as pickled in consols.) What should a person expect to pay for consols which pay 10 a year forever? Assume the first payment is one year from the date of purchase and that interest remains 4% per year, compounded annually. ( denotes pounds, the British unit of currency.)

Figure 10.3 shows the quantity of the drug atenolol in the blood as a function of time, with the first dose at time t = 0. Atenolol is taken in 50 mg doses once a day to lower blood pressure. (a) If the half-life of atenolol in the blood is 6.3 hours, what percentage of the atenolol present at the start of a 24-hour period is still there at the end? (b) Find expressions for the quantities Q0, Q1, Q2, Q3, . . ., and Qn shown in Figure 10.3. Write the expression for Qn in closed form. (c) Find expressions for the quantities P1, P2, P3, . . ., and Pn shown in Figure 10.3. Write the expression for Pn in closed form. 1 2 3 4 5 Q0 t (time, days) q (quantity, mg) Q1 Q2 Q3 Q4 P1 P2 P3 P4 Figure 10.3

One way of valuing a company is to calculate the present value of all its future earnings. A farm expects to sell $1000 worth of Christmas trees once a year forever, with the first sale in the immediate future. What is the present value of this Christmas tree business? The interest rate is 1% per year, compounded continuously.

In Problems 130, indicate whether the statement is true or false. The present value of 3 annual payments of $600, starting now, assuming annual interest rate of 4%, is 600 + 600(1.04)1 + 600(1.04)2 dollars.

In Problems 130, indicate whether the statement is true or false. The present value of 10 annual payments of $600, starting now, assuming annual interest rate of 4%, is 600(1 (1.04)10)/(1 (1.04)1) dollars.

In Problems 130, indicate whether the statement is true or false. If a person consumes a 25-mg tablet of a drug four times throughout the day, at the end of the day the person will have 100 mg of the drug in the body.

In Problems 130, indicate whether the statement is true or false. If the quantity of a drug in the body has reached the steady-state level for a person taking a drug at regular intervals, then the quantity of drug in the persons body stays constant.

In Problems 130, indicate whether the statement is true or false. A person consuming 3micrograms of a toxinwith breakfast each day, of which 5% leaves the body each day, has 3/(1-0.05) micrograms of toxin in the body right after breakfast, in the long run.

In Problems 130, indicate whether the statement is true or false. If a country used 10 billion barrels of oil last year, and oil consumption increases at 2% annually, then over the next 5 years, the total oil consumption will be 10(1.02)(1 (1.02)5)/(1 1.02) billion barrels.

In Problems 130, indicate whether the statement is true or false. In a person taking a constant dose D mg of medication everyday, the steady-state level is the same before and after each daily dose.

In Problems 130, indicate whether the statement is true or false. In a person taking a constant dose D mg of medication every day, at the steady-state level the quantity of the drug eliminated daily is equal to the daily dose D.

In Problems 130, indicate whether the statement is true or false. If a drug is administered intravenously, then a geometric series is a better model than a differential equation for the quantity of drug in the bloodstream.

In Problems 130, indicate whether the statement is true or false. If a certain drug has a half-life of three hours in the body, then nine hours after a dosage of 160 mg, the quantity in the body drops to 20 mg.

In Problems 130, indicate whether the statement is true or false. If a 50-mg injection of a drug is given once every day, and the drug is metabolized at a continuous rate of 5% per day, then the long-term steady-state quantity in the body after injection is 50/(1 e0.05).

In Problems 130, indicate whether the statement is true or false. If a drug is administered intravenously at a rate of 50 mg per day, and the drug is metabolized at a continuous rate of 5% per day, then the long-term steady-state quantity in the body is 1000 mg.