A radioactive material went through a decaying process as given in the following function f(t): f(t) = 5e¬at where a is a constant attribute of the radioactive material and t is the time unit.

The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.

The graph in Figure 19 illustrates the decay of a radioactive substance over t days. Use the graph to estimate the average decay rate from t=5tot=15 .

Newton's law of cooling says that a hot object cools rapidly when the difference between its temperature and that of the surrounding air is large, but the object cools more slowly when it nears room temperature. Suppose a piece of aluminum is removed from an oven and left to cool. The following table gives the temperature A = A(t), in degrees Fahrenheit, of the aluminum t minutes after it is removed from the oven. t = Minutes A = Temperature 0 306 30 150 60 104 90 83 120 75 150 73 180 72 210 72 (a) Explain the meaning of A(75). The expression A(75) is the amount of time it takes for the aluminum to reach 75 degrees Fahrenheit.The expression A(75) is the temperature of the piece of aluminum when the temperature of the oven reaches 75 degrees Fahrenheit.    The expression A(75) is the amount of time it takes for the aluminum to reach 75 degrees Fahrenheit after removed from the oven.The expression A(75) is the temperature in degrees Fahrenheit of the piece of…