Please provide the correct answers for the following questions. Thanks!

Find the mass that remains after t years. Let y(t) be the mass (in mg) remaining after t years. Then we know the following. y(t) = y(0)eht Since the half-life is 30 years, then y(30) = mg. Thus, e30k = Preview Therefore, k = Preview Now, remembering that In a" = n In a and that elz = z, we have y(t) = 110e (t/30) ( -In 2) = Preview mg. How much of the sample remains after 90 years? After 90 years we have the following. y(90) = 110 . 2 Preview mg (Round your answer to two decimal places.) After how long will only 1 mg remain? To find the time at which only 1 mg remains, we must solve 1 = y(t) = 110(2-1/30) ), and so we get the following. t = - 3010g2( Preview