algebra part 1

Question 1 (5 points)

Simplify. Assume that no denominator is equal to zero.

Question 1 options:

Question 2 (5 points)

Find the first five terms of the sequence in which a₁ = –10 and a_n = 4a_{n – 1} + 7, if n ≥ 2.

Question 2 options:

	–10, –33, –125, –493, –1965
	–33, –125, –493, –1965, –7853
	11, 15, 19, 23, 27
	47, –10, –33, –125, –493

Question 3 (5 points)

Simplify the expression.

·

Question 3 options:

	255

Question 4 (5 points)

Simplify the expression.

10
+ 7

Question 4 options:

	70
	3
	17

Question 5 (5 points)

Solve the equation of exponential decay.

The population of a city was 572,000 in 2010. In the 2000 census the population was 607,000. What was the rate of decrease of the population from one census to the next? Round to the nearest percent.

Question 5 options:

	8%
	6%
	3%
	1%

Question 6 (5 points)

Simplify: 81^1/4.

Question 6 options:

	3
	4
	12

Question 7 (5 points)

Simplify. Assume that no denominator is equal to zero.

Question 7 options:

Question 8 (5 points)

Write an equation for the nth term of the sequence 4, 12, 36, 108, …

Question 8 options:

	an = 4(3)n
	an = 3(4)n
	an = 4(3)n – 1
	an = 3(4)n – 1

Question 9 (5 points)

Simplify the expression.

9
(8
+ 9
)

Question 9 options:

	216 +
	216 + 81
	27 + 81
	216 + 9

Question 10 (5 points)

Simplify. Assume that no denominator is equal to zero.

Question 10 options:

Question 11 (5 points)

Simplify the expression.

10
+ 5
– 8
– 3

Question 11 options:

	2 + 2
	2 + 2
	80 – 15
	18 + 8

Question 12 (5 points)

Simplify. Assume that no denominator is equal to zero.

Question 12 options:

Question 13 (5 points)

Simplify: .

Question 13 options:

	160
	3
	2

Question 14 (5 points)

Solve the equation of exponential decay.

The population of a city is expected to be 440,000 in 2020. This is a decline of 12% from 2010 to 2020. Assuming this continued what would the population of the city be in 2040? Round to the nearest ten thousand.

Question 14 options:

	340,000
	300,000
	390,000
	410,000

Question 15 (5 points)

Simplify the expression.

Question 15 options:

Question 16 (5 points)

Find the first five terms of the sequence in which a₁ = 6 and a_n = –3a_{n – 1} – 12, if n ≥ 2.

Question 16 options:

	–30, 78, –246, 726, –2190
	6, –30, 78, –246, 726
	6, 6, –30, 78, –246
	–15, –18, –21, –24, –27

Question 17 (5 points)

Determine whether the data in the table display exponential behavior. Explain why or why not.

x	3	2	1	–1
y	8	2	0.5	0.125

Question 17 options:

	No; the domain values are at regular intervals and the range values have a common factor 0.25.
	No; the domain values are not at regular intervals although the range values have a common factor.
	Yes; the domain values are at regular intervals and the range values have a common factor 4.
	Yes; the domain values are at regular intervals and the range values have a common factor 0.25.

Question 18 (5 points)

Solve the equation of exponential decay.

A car sells for $25,000. If the rate of depreciation is 15%, what is the value of the car after 7 years? Round to the nearest hundred.

Question 18 options:

	$8,000
	$9,400
	$7,400
	$9,800

Question 19 (5 points)

Simplify. Assume that no denominator is equal to zero.

Question 19 options:

Question 20 (5 points)

Simplify. Assume that no denominator is equal to zero.

(
a
⁵
b
³)(
a
³
b
⁵)

Question 20 options:

	a15b15
	a15b8
	a8b8
	a8b15

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