A laboratory has a 75-gram sample of radioactive material. The half-life of the material is 10 days. What is the mass of the laboratory’s sample remaining after 30 days?
A9.375 grams
B11.25 grams
C12.5 grams
D22.5 grams
Mathematics · Question Bank
Differential Equations
42 questions · page 3 of 3. Answer in your head first, then check the solution.
A motorboat weighs 32,000 lb and its motor provides a thrust of 5,000 lb. Assume that the water resistance is 100 pounds for each foot per second of the speed v of the boat. Then \(1{,}000\dfrac{dv}{dt} = 5{,}000 - 100v\). If the boat starts from rest, what is the maximum velocity that it can attain?
A20 ft/s
B25 ft/s
C40 ft/s
D50 ft/s