Posted: April 9th, 2022

Math

1. Given that y = 1.6
−x
, write an equivalent equation in the form y = b
x
, 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 = 1000e
0.10x
.
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.)
e
9x + 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 = 1500e
0.07x
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 = 1,500e
0.053t
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) = 10,020e
0.02292t
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

————

1. Assume y = 1.6 x.

, construct an analogous equation of the form y = b

x

, where 0 b 1

y=_____________

2. If $1200 is invested for x years at 8% compounded quarterly, what is the future value?

The following equation represents the end outcome.

1200 = S (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.)

$________________

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