Math 155- Lab Assignment (Exponential Functions) . Suppose that $5000 is invested and pays 6.5% per year under the following compounding options. . Compounded annually . Compounded quarterly . Compounded monthly . Compounded daily . Compounded continuously Determine the total amount in the account after 10 year with each option. . The half-life of radium 226 is 1620 yr. In a sample originally having 1 9 of radium 226, the amount A(t) (in grams) of radium 226 present after t years is given by A(!) = ()71620 where t is the time in years after the start of the experiment. How much radium will be present after . 1620 yr? 3240 yr? 4860 yr?. The function defined by A(t) = 100 0.0318t approximates the equivalent amount of money needed t years after the year 2010 to equal $100 of buying power in the year 2010. The value 0.0318 is related to the average rate of inflation. . Evaluate A(15) and interpret its meaning in the context of this problem. Verify that by the year 2032, more than $200 will be needed to have the same buying power as $100 in 2010. 300 250 200 Amount ($) 150 100 0 5 10 15 20 25 30 Years after 2010 . A veterinarian depreciates a $10,000 X-ray machine. He estimates that the resale value V(t) (in $) after t years is 90% of its value from the previous year. Therefore, the resale value can be approximated by V(t) = 10,000(0.9). Find the resale value after 4 yr. . If the veterinarian wants to sell his practice 8 yr after the X- ray machine was purchased, how much is the machine worth? Round to the nearest $100