# math

please fill in the blank

1. Given that y = 1.6−x, write an equivalent equation in the form y = bx, with 0 < b < 1

y=_____________

2. If \$1200 is invested for x years at 8%, compounded quarterly, the future value that
will result is represented by the following equation.

S = 1200(1.02)4x

What amount will result in 4 years? (Round your

answer to the nearest

cent.)

\$______________

3. The purchasing power P of a fixed income of \$20,000 per year (such as a pension)
after t years of 7% inflation can be modeled by

P = 20,000(1.07)−t.
(a) Find the purchasing power after 5 years. (Round your answer to the nearest
dollar.)

\$

_______________

(b)Find the purchasing power after 20 years. (Round your answer to the nearest
dollar.)

\$

________________

4. If \$1000 is invested for x years at 10%, compounded continuously, the future value

that results is
S = 1000e0.10x.

What amount will result in 3 years? (Round your answer to the nearest cent.)

\$______________

5. Solve the equation.
log(x) = 6

x=__________

6. Solve for x by writing the equation in exponential form.
log(3x − 4) = 2

x=______________

7. Solve for x by writing the equation in exponential form. (Round your answer to three
decimal places.)

ln(2x + 4) = 2.3
x=_____________

8. Write the equation in logarithmic form and solve for x. (Round your answer to three
decimal places.)

e9x + 5 = 0.51

x=____________

9. Solve the equation. Give your answer correct to 3 decimal places.
95,000 = 10,000(1.02)3x

x = ____________

10. Solve the equation. Give your answer correct to 3 decimal places.
10,000 = 1500e0.07x

x = _____________

11. Solve the equation. Give your answer correct to 3 decimal places.
82 = 100 − 100e−0.07x

x = _____________

12. The sales decay for a product is given by S = 80,000e−0.5x, where S is the monthly
sales and x is the number of months that have passed since the end of a promotional
campaign.

(a)What will be the sales 6 months after the end of the campaign? (Round your
answer to two decimal places.)

\$______________
(b)How many months after the end of the campaign will sales drop below \$1,000, if
no new campaign is initiated? (Round up to

the nearest whole number.)

_____________months

13. For the years from 2002 and projected to 2024, the national health care
expenditures H, in billions of dollars, can be modeled by

H = 1,500e0.053t

where t is the number of years past 2000.† In what year are national health care
expenditures expected to reach \$4.0 trillion (that is, \$4,000 billion)?

_______________

14. Disposable income is the amount available for spending and saving after taxes have
been paid and is one gauge for the state of the economy. Using U.S. Energy
Administration data for selected years from 2010 and projected to 2040, the total
U.S. disposable income, in billions, can be modeled by

D(t) = 10,020e0.02292t

where t is the number of years past 2010. In what year is disposable income

predicted to be \$15 trillion (that is, \$15,000 billion)?

________________

15. The demand function for a certain commodity is given by p = 100e−q/2. (p is the price

per unit and q is the number of units.)

(a)At what price per unit will the quantity demanded equal 6 units? (Round your

answer to the nearest cent.)

\$_______________

(b)If the price is \$1.79 per unit, how many units will be demanded, to the nearest

unit?

_

______________units

16. The total cost function for a product is C(x) = 650 ln(x + 10) + 1700

where x is the number of units produced.

(a) Find the total cost of producing 100 units. (Round your answer to the nearest

cent.)

\$__________________

(b)Producing how many units will give total costs of \$7500? (Round your answer to

the nearest whole number.)
______________units

17. Suppose the supply of x units of a certain product at price p dollars per unit is given

by p = 16 + 6 ln(2x + 1).

How many units of this product would be supplied when the price is \$52 each?

(Round your answer to the nearest whole number.)

______________units

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