14. The concentration of a drug in the body decreases exponentially after a dosage is given. In one clinical study, adult subjects averaged 11 micrograms/milliliter (mcg/mL) of the drug in their blood plasma 1 hr after a 1000-mg dosage and 2 micrograms/milliliter 4 hr after dosage. a) Find the value k, and write an equation for an exponential function that can be used to predict the concentration of the drug, in micrograms/milliliter, t hours a 1000-mg dosage. b) Estimate the concentration of the drug 3 hr after a 1000-mg dosage. c) To relieve a fever, the concentration of the drug should go no lower than 2 mcg/mL. After how many hours will a 1000-mg dosage drop to that level? aj k = (Round to three decimal places as needed.) Choose the correct equation below. O A. P(t) = 19.4e - 0.68at OB. P(t) = 11 e - 0.308: O C. P(t) = 21.400e - 1.704t O D. P(t) = 17.400 e - 0.508t DE. P(t) = 21.400e - 0.508t OF. P(t) = 11e - 0.448: O G. P(t) = 19.4e - 0.508t OH. P(t) = 19.4e - 1.704t b) The concentration of the drug after 3 hr will be about mcg/mL. (Round to one decimal place as needed.) c) After about hr the concentration of the drug will have dropped to 2 mog/mL. Round to the nearest integer as needed.) 15. The population of a country dropped from 51.4 million in 1995 to 45.8 million in 2008. Assume that P(t), the population, in millions, t years after 1995, is decreasing according to the exponential decay model a) Find the value of k, and write the equation. b) Estimate the population of the country in 2017. c) After how many years will the population of the country be 2 million, according to this model? ) Select the correct answer below and fill in the answer box to complete your choice. (Round to four decimal places as needed.) O A. P(t) =51.48 - 51.4 O B. P(t) = 45.Be - ( 45.8 O c. P(1) = - O D. P(t) = 45.Be - b) The population of the country in 2017 will be about million. (Round to one decimal place as needed.) c) According to this model, years after 1995 the population will be 2 million. Round to the nearest whole number as needed.] 16. A coroner arrives at a murder scene at 11 p.m. She finds the temperature of the body to be 84.9"F. She waits one hour, takes the temperature again, and finds i be 80.6"F. She notes that the room temperature is 63"F. Assuming that the temperature of the body was 98.6"F when the murder occured, when was the murde committed? The murder was commited at approximately approximately (Do not round until the final answer. Then round to the nearest hour.) (1) O am. O p.m. 17. For the scatterplot on the right, determine which, if any, of these functions might be used as a model for the data. 15- Quadratic: f(x) = ax + bx + c Polynomial, not quadratic # of fruit flies (hundreds 10- Exponential: f(x) = apkx, k> 0 Exponential: f(x) = ae - kx, k > 0 a Logarithmic: f(x) = a + bInx Logistic: f(x) = 1+be - kx 12345 x Day Which of the functions above might be used as a model for the data? O A. Polynomial, not quadratic O B. Logarithmic: f(x) = a + b Inx O c. Logistic: f(x) = 1+be - kx O D. Exponential: f(x) = ae -kx, k>0 O E. Exponential: f(x)= apki, k>0 OF. Quadratic: f(x) = ax"+ bx+ c
