10. A person deposits $1000 in an account that yields 9% pounded anually. a) Set upa recurrence relation for the amount in the account at the end ofn years. b) Find an explicit formula for the amount in the account at the end ofn years. c) How much money will the account contain after 100 years? 12. Assume that the population of the world in 2002 was billion and is growing at the rate of % a year. a) Set upa recurrence relation for the population of the world n years after 2002. b) Find an explicit formula for the population of the world n years after 2002. c) What will the population of the world be in 2022? 18. a) Find a recurrence relation for the number of permutations ofa set with n elements. b) Use this recurrence relation to find the number of permutations ofa set with n elements using iteration. 24. a) Find a recurrence relation for the number of bit strings of length n that contain three consecutive 0s. b) What are the initial conditions? c) How many bit strings of length seven contain three consecutive 0s? 26. a) Find a recurrence relation for the number of bit strings that contain the string 01. b) What are the initial conditions? c) How many bit strings of length seven contain the string 01? 28. a) Find a recurrence relation for the number of ways to climb n stairs if the person climbing the stairs can take one, two, or three stairs ata time. b) What are
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