6:37 AM Wed Apr 15 ll LTE © 100% April 14.pdf Look at the notes on exponential and logs notes and answer the following questions, and submit the work as PDF file 26. A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t) = 13e-0.015: where m{t) is measured in kilograms. (a) Find the mass at time t = 0. (b) How much of the mass remains after 45 days? 27. Radioactive iodine is used by doctors as a tracer in diag- nosing certain thyroid gland disorders. This type of iodine decays in such a way that the mass remaining after t days is given by the function m{t) 6e -0.0871 where m(t) is measured in grams. (a) Find the mass at time t = 0. (b) How much of the mass remains after 20 days? 28. A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is proportional to her velocity, and the constant of proportionality is 0.2. It can be shown that the downward velocity of the sky diver at time t is given by v1) = 80(1 – e -02) %3D (d) After how many hours will thế fiumbe reach 10,000? 16. The count in a culture of bacteria was 400 after 2 hours and 25,600 after 6 hours. (a) What is the relative rate of growth of the bacterium population? Express your answer as a percentage. (b) What was the initial size of the culture? (c) Find a function that models the number of bacteria n(r) after t hours. 29. A hot bowl of soup is served at a dinner party. It starts to cool according to Newton's Law of Cooling so that its tem- perature at time t is given by T(1) = 65 + 145e-0.05: where t is measured in minutes and T is measured in °F. (a) What is the initial temperature of the soup? (b) What is the temperature after 10 min? (c) After how long will the temperature be 100°F?

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