I’m trying to learn for my Algebra class and I’m stuck. Can you help?
Question 1 (5 points)
Simplify. Assume that no denominator is equal to zero.
Question 2 (5 points)
Find the first five terms of the sequence in which a_{1} = â€“10 and a_{n} = 4a_{n} _{â€“ 1} + 7, if n â‰¥ 2.
Question 3 (5 points)
Simplify the expression.
Â·
Question 4 (5 points)
Simplify the expression.
10
+ 7
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 6 (5 points)
Simplify: 81^{1/4}.
Question 7 (5 points)
Simplify. Assume that no denominator is equal to zero.
Question 8 (5 points)
Write an equation for the nth term of the sequence 4, 12, 36, 108, …
Question 9 (5 points)
Simplify the expression.
9
(8
+ 9
)
Question 10 (5 points)
Simplify. Assume that no denominator is equal to zero.
Question 11 (5 points)
Simplify the expression.
10
+ 5
â€“ 8
â€“ 3
Question 12 (5 points)
Simplify. Assume that no denominator is equal to zero.
Question 13 (5 points)
Simplify: .
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 15 (5 points)
Simplify the expression.
Question 16 (5 points)
Find the first five terms of the sequence in which a_{1} = 6 and a_{n} = â€“3a_{n} _{â€“ 1} â€“ 12, if n â‰¥ 2.
Question 17 (5 points)
Determine whether the data in the table display exponential behavior. Explain why or why not.
x |
3 |
2 |
1 |
â€“1 |
y |
8 |
2 |
0.5 |
0.125 |
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 19 (5 points)
Simplify. Assume that no denominator is equal to zero.
Question 20 (5 points)
Simplify. Assume that no denominator is equal to zero.
(
a
^{5}
b
^{3})(
a
^{3}
b
^{5})