Calc 2 assesments

I) In the year 2000, the population of a small town was 5000 people. In the year 2010, the population was 0000 people. a) 1st t be the number of years after the year 2000. Find a Monnla of the form y = yo • ekt that predicts Mc population t years after 2000. (Use at least 4 significant digits.) b) Predict the population of the town in the year 2015. 2) A radioactive substance has a half-life of 500 years. How long does it take a 100 mg sample M decay to 30 mg? 3) Find the length of the curve y= 40I1' , 0 <x <2 4) Find the solution of the differential equation that satisfies the initial condition: dy • sin 5) Find the solution of the differential equation that satisfies the initial condition: ÷"„ y • r(0)= 6) A tank initially contains 30 kg of salt dissolved in 2000 L of water. Brine that contains 0.02 kg of salt per liter of water enters the tank at a rate of 20 Lrmin. The solution is kept thoroughly mixed and draws from the tank at a rate M20 Umiv. Sind a formula for the amount of salt (n kg) remaining after r minutes. 7) Consider the polar curve r = 3 — 3 cos a) Graph the curve on the polar graph paper on page 2. b) Find the area inside the curve. You may evaluate the necessary integral on your calculator. 8) Consider the polar curve r 5 sin(38) a) Graph the curve on the polar graph paper on page 2. Your graph should accurately reflect the location of the tip of each loop. b) Find the area insideanelcoo of the curve. You may evaluate the necessary integral on your calculator.