Suppose you owe $500 on your credit card and you decide to make no new purchases and to make the minimum monthly payment on the account. Assuming that the interest rate on your card is 1% per month on the unpaid balance and that the minimum payment is 2% of the total (balance plus interest), your balance aer t months is given by B(t) = 500(0.98981). Find your balance at each of the given times. Complete parts (a) through (e) below. (a) six months After six months, the balance is $|:. (Round to the nearest cent as needed.) The annual amount of energy produced in a country from dry natural gas (in trillion cubic feet) can be approximated by the function g(t)=14.54(1.044)t, where t= 10 corresponds to the year 2010. (a) Find the amount of dry natural gas energy produced in 2016. (b) If the model continues to be accurate, project the amount of dry natural gas energy produced in 2025. (a) The amount of dry natural gas energy produced in 2016 was :I trillion cubic feet. (Round to the nearest hundredth as needed.) The annual amount of crude-oil production in a country (in millions of barrels) can be approximated by the function f(t) = 874(1.094)t, where t= 8 corresponds to the year 2008. (3) Find the amount of production in 2013. (b) If the trend continues, nd the amount of production in 2018. (a) The amount of production in 2013 was million barrels. (Round to the nearest whole number as needed.) The table shows the total assets (in trillions) held in a foreign bank for the given years. Complete parts (a) through (c) below. Year |2000 | 2005 | 2007 | 2009 | 2011 |2013 | 2015 Assets | 15 | 41 | 54 | 79 |117 | 151 | 199 (a) Find an exponential model of the form f(t) = yob' for these data, where t = 0 corresponds to the year 2000. If you do not have suitable technology, use the rst and last data points to nd a function. If you have a graphing calculator or other suitable technology, use exponential regression to nd a function. t The exponential model for the dam is f(t) =D(D) . (Round to three decimal places as needed.) It has been found that a worker new to the operation of a certain task on the assembly line will produce P(t) items on day t, where P(t) = 29 - 29 e _ 0.3t_ How many items will be produced on the 1st day, and what is the maximum number of items, according to the function, the worker can produce? The worker will produce '1 items on the rst day. (Round to the nearest whole number.) 121 1+3.45e The amount of money a certain government spent on food and nutrition assistance (in billions of dollars) can be approximated by the function f(x) = corresponds to the year 2000. Use a graphing calculator or other technology to complete parts (a) and (b) below. .3 - 0.248x ' where x = 0 (a) Find the amount spent in 2000 and 2015. Write the expression that can be used to nd the amount spent in the year 2000 (in billions of dollars). (Do not evaluate.)