There are 500 bees in a colony at a nearby beekeeper’s farm. The current bee virus has caused the colony to decline by 4% per week in population. Write an exponential function that represents the population of bees in the colony where t is the number of weeks since the virus began. What is the expected population in 22 weeks?

(i need the function and # of bees after 22 weeks

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e.g. 98.76543).

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.

1) prove that 731^3−631^3 is divisible by 100 2) prove that 99^3−74^3 is divisible by 25