Chapters 4/5

Exponents/Logs

100

16^x+31 = 64^x+1

X=59

200

log(4x) = log17

X= log17/log4

300

8^x=33

x = log₈33

400

log(7x+6) = 3

x=142

500

log(38x+6)=log3

x=-3/38

Arithmetic Series Sequences

100

Is the following sequence Arithmetic - 1, 3,5,7,9,11

Yes, because you are adding 2 everytime

200

What is the 7th term of the sequence - 8, 80, 152

440

300

What is the arithmetic sequence formula

a_n=a₁+(n-1)d

400

Solve: Sigma 9 on top and n=1 on bottom, (n=700)

6345

500

Solve sigma 8 on top, n=1 on the bottom 60+n

516

Geometric Sequence

100

Is this sequence Geometric 3,6,12,24,48,96

yes, you are multiplying by 2 every time. 

200

What is the infinite geometric series formula

a₁/1-r

300

What is the finite geometric series formula

a(1-rⁿ)/(1-r)

400

rewrite this in sigma notation 2,6,18,54

sigma 3 on top, K=0 on bottom 2(3^k)

500

What is the geometric series of sigma 4 on top n=1 on the bottom 2(3^n-1)

2,6,18,54

Limits

100

solve as the limit approaches infinity

n²-3n+1/n+8 

No solution

200

solve the limit as n approaches infinity

n²+1/n2

1

300

Solve the limit as n approaches infinity

4n²+2n+4/n²+2

4/3

400

Solve as the limit goes to infinity ((x²+329)/(x⁴)) +8

8

500

Solve as the limit approaches 3

x²+15x+54/6x²+216

-1

Permutation/Combinations

100

Does order matter for a permutation

yes

200

Does order matter for a combination

No

300

A team of 15 basketball players need a starting 5 but the team is really bad and everyone is the same height so it does not matter who plays what position or which 5 are on the court.

₁₅C₅  3003

400

A marathon has 100 runners and the top ten will receive the same amount of money each.   

₁₀₀C₁₀    1.73*10^13

500

There are 200 students at Moeller and three get selected for Captain and vice captain, and third captain.

₂₀₀P₃   7880400