Question 1:

Suppose that the amount, in grams, of polonium 210 present in a given sample is determined by the function defined by T A(t) = 401e -0.054, where t is the time in years. Find the amount present in a sample of 401 grams after 25 years. (SThe time, t, in years for an amount increasing at a rate of r (in decimal form) to double is given by t= In 2 In (1+r) This is called the doubling time. Find the doubling time to the nearest tenth for an investment at an interest rate of 4% = 0.04. The doubling time is years. (Round to the nearest tenth of a year.)The hydrogen ion concentration, [H * ], in a certain cleaning compound is [H * = 3.3 x 10 . Use the formula pH = - log [H * ] to find the pH of the cleaning compound. The pH is approximately (Round to the nearest tenth as needed.)The value V of a bank account in which $450 is invested at 9.00% interest, compounded annually is given by the equation below where t is the time in years. Find the value of the account after 7 years. V = 450(1.0900) The value of the account after 7 years is about $ (Round to the nearest cent as needed.)Solve the given problem. If x = In 2 and y = In 5, express In 100 in terms of x and y. In 100 = (Simplify your answer.)If interest is compounded continuously (daily compounded interest closely approximates this), a bank account can double in t years according to the equation i = In 2 t where i is the interest rate expressed in decimal form. What interest rate is required for an account to double in 11 years? i=% (Do not round until the final answer. Then round to the nearest tenth as needed.)