FlamerHead

A young person with no initial capital invests k dollars per year in a retirement account at an annual rate of return 0.04. Assume that investments are made continuously and that the return is compounded continuously.

Determine a formula for the amount of money A(T) in the account after T years (this will involve the parameter k):

A(T) =_____________

A wealthy patron of a small private college wishes to endow a chair in mathematics with a gift of G thousand dollars. Suppose the mathematician who occupies the chair is to receive $80 thousand dollars per year in salary and benefits. If money costs 7% per year compounded continuously, what is the smallest possible value for G?

G = _________ thousand dollars

A machine at t years old generates revenue @ the rate:

R'(t)=5950-14t^2 dollars/year

The operating and servicing costs accumulate @ the rate:

C'(t)=3300+12t^2 dollars/year

How many years pass before the profitability of the machine begins to decline?

_____ years

At age 30, John makes annual deposits of $2400 into a bond fund that pays 9% annual interest compounded continuously. The deposits are made as continuous income flow, so HOW MUCH MONEY WILL BE IN THE ACCOUNT IF HE RETIRES AT AGE 55?

_______dollars

A company is selling a 10-year franchise.

t years from now the franchise will generate profit at the rate of: f(t)=17500 dollars/year

If the annual interest rate remains fixed at 8% compounded continuously, what is the present value of the franchise?

________dollars

Money is transferred into an account at the rate of R(t) = 1500 te^(−0.9t) dollars per year for 5 years. If the account pays 7% interest compounded continuously, how much will accumulate in the account over a 5-year period?

A manufacturer has found that marginal cost is (0.2 q + 1)e^0.02 q dollars per unit when q units have been produced. What is the total cost of producing the first 15 units?

Suppose that a particular industrial machine, when it is t years old, generates revenue at the rate R′(t)=5950−14t^2 dollars per year and that operating and servicing costs accumulate at the rate C′(t)=3300+12t^2 dollars per year.

a. How many years pass before the profitability of the machine begins to decline?

The management of a national chain of fast-food outlets is selling a 10-year franchise in Cleveland, Ohio. Past experience in similar localities suggests that t years from now the franchise will be generating profit at the rate of f(t) = 17500 dollars per year. If the prevailing annual interest rate remains fixed at 8 percent compounded continuously, what is the present value of the franchise?

Suppose D(q) = 6(49−q^2) is the price (dollars per unit) at which q units of a particular commodity will be demanded by the market (that is, all q units will be sold at this price).

a. Find the price p0 at which 6 units will be demanded. ANSWER: ______

Suppose S(q) =18+10e^(0.09q) is the price (dollars per unit) at which q units of a particular commodity will be supplied to the market by producers.

a. Find the price p0 at which 15 units will be supplied.

Answer: p0 = _________ dollars per unit.

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.

y=e^(3x)

y=e^(7x)

x=1

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.

y=4x

y=6x^2

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.

y=e^(3x)

y=e^(7x)

x=1

Find the area of the region enclosed by

y=6x^2 and y=x^2+15.

AREA= _________

Evaluate the definite integral

e^3

⌠

⌡(dx/(x(1+lnx)))

1

Find area of the region under the curve y = 3 x^3 − 9 and above the x-axis, for 3 ≤ x ≤ 6.

area = _________

2

⌠

⌡ ((e^(3/x))/(x^2)) dx

1

(e^3)

⌠

⌡ ((dx)/(x(1+lnx))) dx

1

EVALUATE

1

⌠

⌡ ((2e^(10x)-5)/(e^(2x))) dx

0

Evaluate the definite integral... please show steps :)