Hi i need help with questions from a study guide I got wrong.

1.A playground is being designed where children can interact with their friends in certain combinations.

If there is 1 child, there can be 0 interactions.

If there are 2 children, there can be 1 interactions.

If there are 3 children, there can be 4 interactions.

If there are 4 children, there can be 9 interactions.

How many interactions will there be for 6 children?

11

16

25

36

2.A playground is being designed where children can interact with their friends in certain combinations.

If there is 1 child, there can be 0 interactions.

If there are 2 children, there can be only 1 interaction.

If there are 3 children, there can be 5 interactions.

If there are 4 children, there can be 14 interactions.

Which recursive equation represents the pattern?

a_n= a_{n - 1}+ 2^{(n - 1)}

a_n= a_{n - 1}+ (n - 1)²

a_n= a_{n - 1}+ 2(n - 1)

a_n= a_{n - 1}+ (2n - 1)

3.Sheryl purchased a plot of land for $32,500. The land appreciates about 4.9% each year. What is the value of the land after eleven years?

$50,017.50

$18,701.18

$55.006.46

$33,989.96

4.Lowell purchased a motorcycle for $17,011. It depreciates about 3.9% each year. What is the value of the motorcycle after eight years?

$12,374.19

$16,573.71

$11,703.57

$23,102.25

5.The yearly attendance at a local movie theater is 68,000 and grows continuously at a rate of 3.5% each year. What is the approximate attendance at the movie theater in eight years?

69,603

89,543

89,973

87,040

6.The number of customers that visit a local small business is 46,900 and has been continuously declining at a rate of 3.2% each year. What is the approximate number of customers that visit the business in 8 years?

36,307

33,393

60,583

36,156