# Expert Answers

What is the chance that 1 item out of 30 would remain as 1 of the last 2 items if an item is removed 1 at a time?

∫ r^5(3+r^6)^6dr=?

2∫ (dx/2x+1)=?

3∫ [(e^y)/7+e^y] dy=?

4.∫[(x-4)^2]dx

5. D(x) is the price in dollars per unit that consumers are willing to pay for x units of an item, and S(x) is the price in dollars per unit that producers are willing to accept for x units. Find (a) the equilibrium point. (b) the consumer surplus at the equilibrium point, and (c) the producer surplus at the equilibrium point.

D(x)= -(4/9)x+16, S(x)=(1/3)x+2

6. D(x) is the price, in dollars per unit that consumers are willing to pay for z units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units find (a) the equilibrium point and (c) the producer surplus at the equilibrium point.

D(x)=(x-4)^2, S(x)=(x^2)+2x+6

Find the future value P of the amount P =$100,000 invested for time period t=6 years at interest rate k=3% compounded continuously. 0

If $100,000 is invested what is the amount accumulated after 6 years?

8. Find the present value (P)of the amount P=$200,000 due t=6 years in the future and invested at interest rate k=3% compounded continuously (0)

for 7 and 8 the 0 is below the P. In 8 they are marked with ()

Find the accumulated future value of the continuous income stream at rate R(t) for the given time T, and interest rate k, compounded continuously

R(t) = $400,000, T = 16 years, k = 4%

the accumulated future value is $?

for 5 was 72, and 54 exactly

10. in 18 years Anthony Douglas is to receive $100,000 under the terms of a trust established by his grandparents. Assuming an interest rate of 5.4% compounded continuously what is the present value of Anthony's legacy?

the present value of the legacy is $?

11.At age 35, Preston earns his MBA and accepts a position as vice president of an asphalt company. Assume that he will retire at the age of 65, having received an annual salary of $90,000 and that the interest rate is 5% compounded continuously

A) What is the accumulated present value of his position?

B)what is the accumulated future value of his position?

12 In the year 2000(t=0) the world reserves of natural gas were approximately 6112 trillion cubic feet. In that same year, the world consumption of natural gas was approximately 110.1 trillion cubic feet, and was growing exponentially at about 2.6% per year. If demand continues to grow at this rate and no new reserves of natural gas are found, in what year will the world reserves of this resource be depleted?

∫ r^5(3+r^6)^6dr=?

2∫ (dx/2x+1)=?

3∫ [(e^y)/7+e^y] dy=?

4.∫[(x-4)^2]dx

5. D(x) is the price in dollars per unit that consumers are willing to pay for x units of an item, and S(x) is the price in dollars per unit that producers are willing to accept for x units. Find (a) the equilibrium point. (b) the consumer surplus at the equilibrium point, and (c) the producer surplus at the equilibrium point.

D(x)= -(4/9)x+16, S(x)=(1/3)x+2

6. D(x) is the price, in dollars per unit that consumers are willing to pay for z units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units find (a) the equilibrium point and (c) the producer surplus at the equilibrium point.

D(x)=(x-4)^2, S(x)=(x^2)+2x+6

Find the future value P of the amount P =$100,000 invested for time period t=6 years at interest rate k=3% compounded continuously. 0

If $100,000 is invested what is the amount accumulated after 6 years?

8. Find the present value (P)of the amount P=$200,000 due t=6 years in the future and invested at interest rate k=3% compounded continuously (0)

for 7 and 8 the 0 is below the P. In 8 they are marked with ()

Find the accumulated future value of the continuous income stream at rate R(t) for the given time T, and interest rate k, compounded continuously

R(t) = $400,000, T = 16 years, k = 4%

the accumulated future value is $?

for 5 was 72, and 54 exactly

10. in 18 years Anthony Douglas is to receive $100,000 under the terms of a trust established by his grandparents. Assuming an interest rate of 5.4% compounded continuously what is the present value of Anthony's legacy?

the present value of the legacy is $?

11.At age 35, Preston earns his MBA and accepts a position as vice president of an asphalt company. Assume that he will retire at the age of 65, having received an annual salary of $90,000 and that the interest rate is 5% compounded continuously

A) What is the accumulated present value of his position?

B)what is the accumulated future value of his position?

12 In the year 2000(t=0) the world reserves of natural gas were approximately 6112 trillion cubic feet. In that same year, the world consumption of natural gas was approximately 110.1 trillion cubic feet, and was growing exponentially at about 2.6% per year. If demand continues to grow at this rate and no new reserves of natural gas are found, in what year will the world reserves of this resource be depleted?

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