Jake forgot to replace the cap on a bottle of cologne. The cologne began to evaporate at the rate of 18% per day. If the original amount of cologne in the bottle was 50 grams, which of the following graphs best represents the amount of cologne f(x) remaining in the bottle after x days? (1 point) graph of exponential function going down from left to right in quadrant 1 through the point 0, 30 and approaching the x axis graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis graph of function f of x equals 50 multiplied by 0.82 to the power of x graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis

In january 2010, you began a one-year study of tuberculosis (tb) in a subsidized housing community in the lower east side of new york city. you enrolled 500 residents in your study and checked on their tb status on a monthly basis. at the start of your study on january 1st, you screened all 500 residents. upon screening, you found that 30 of the healthy residents had been vaccinated for tb and therefore were not at risk. another 20 residents already had existing cases of tb on january 1st. on february 1st, 5 residents developed tb. on april 1st, 10 more residents developed tb. on june 1st, 10 healthy residents moved away from new york city and were lost to follow-up. on july 1st, 10 of the residents who had existing tb on january 1st died from their disease. the study ended on december 31, 2010. assume that once a person gets tb, they have it for the duration of the study, and assume that all remaining residents stayed healthy and were not lost to follow-up. is the subsidized housing community in the lower east side of new york city a dynamic or fixed population? briefly explain the rationale for your answer. dynamic population it can changeable people can move out and move in into the population of a subsidized housing what was the prevalence of tb in the screened community on january 1st? prevalence = 30/500 0.06= 6% what was the prevalence of tb on june 30th? prevalence= 40/450=0.08= 8.88% what was the cumulative incidence of tb over the year? cumulative incidence = number of new cases/number in candidate population)over specified time period 10/450 = 2.2% suppose that you wanted to calculate the incidence rate of tb in the study population. calculate the amount of person-time that would go in the denominator of this incidence rate. be sure to show your work.

Interpret the following expression (5y^2-7)^3/(2y)^2

Problem 2. find the exact value of the remaining trigonometric functions. sketch theangle 8 for each problem. (3 points each)(a) tan 0 =o is in quadrant 2