A certain small country has $10 billion in paper currency in circulation, and each day $50 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Since both old bills and new bills will come into the banks while the new currency is gradually introduced, we will need to solve a differential equation to track the amount of new currency in circulation at a given time. Let x (t) denote the amount of new currency, in billions of $, in circulation after t days. We've shown that new currency is introduced at the rate 10 - x (t) / 10 0.05, which simplifies to 0.005 (10 - x (t)). This justifies that x (t) satisfies the differential equation dx / dt = 0.005 (10 - x). (a) Solve the differential equation to find x (t). (b) At what time t will new bills make up 90% of the currency in circulation?

(c) compare the results of parts (a) and (b). in general, how do you think the mode, median, and mean are affected when each data value in a set is multiplied by the same constant? multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c. multiplying each data value by the same constant c results in the mode, median, and mean remaining the same. multiplying each data value by the same constant c results in the mode, median, and mean decreasing by a factor of c. there is no distinct pattern when each data value is multiplied by the same constant. (d) suppose you have information about average heights of a random sample of airline passengers. the mode is 65 inches, the median is 72 inches, and the mean is 65 inches. to convert the data into centimeters, multiply each data value by 2.54. what are the values of the mode, median, and mean in centimeters? (enter your answers to two decimal places.) mode cm median cm mean cm in this problem, we explore the effect on the mean, median, and mode of multiplying each data value by the same number. consider the following data set 7, 7, 8, 11, 15. (a) compute the mode, median, and mean. (enter your answers to one (1) decimal places.) mean value = median = mode = (b) multiply 3 to each of the data values. compute the mode, median, and mean. (enter your answers to one (1) decimal places.) mean value = median = mode = --