1) In the year 2000, the population of a small town was 5000 people. In the year 2010, the
population was 6000 people.
a) Let t be the number of years after the year 2000. Find a formula of the form y = yo – e’“
that predicts the 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
to decay to 30 mg?
3) Find the length ofthe curvey = 4×3”, 0 ≤ x ≤ 2
4) Find the solution of the differential equation that satisfies the initial condition:
dy x – sin x
a – T. “0) – 9
5) Find the solution of the differential equation that satisfies the initial condition:
dy 2
E-y 3x, y(0)-10
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 Umin. The solution is kept
thoroughly mixed and drains from the tank at a rate of 20 L/min. Find a formula for the
amount of salt (in kg) remaining after 1 minutes.
7) Consider the polar curve 7′ = 3 – 3 cos 0
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 = S sin(36)
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 inside one loop of the curve. You may evaluate the necessary integral on
your calculator.