There are 1,000 fish in a lake. each year the population declines by 15%, but afterward, the lake is restocked with 500 additional fish. write a recursive rule to find the number of fish in the lake for any year.

Arandom sample of n = 25 observations is taken from a n(µ, σ ) population. a 95% confidence interval for µ was calculated to be (42.16, 57.84). the researcher feels that this interval is too wide. you want to reduce the interval to a width at most 12 units. a) for a confidence level of 95%, calculate the smallest sample size needed. b) for a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.