Q1: The population of Toronto was 2 770 000 in 1975 and 3 133 000 in 1982. Use an exponential growth model to estimate the population in 2021.
Q2: A bacteria culture starts off with 100 bacteria and has grown to 300 bacteria after an hour. Find a formula for the population after t hours (assuming the growth rate is proportional to the size).
Q3: Let \(P_1\) and \(P_2\) denote the population of two types of bacteria. If \(P_1(0) = 100\), \(P_2(0) = 50\), and \(\frac{dP_1}{dt} = -0.3P_1\) and \(\frac{dP_2}{dt} = 0.5P_2\), when are their populations equal?
Q4: A radioactive material’s mass can be modelled by \(\frac{dm}{dt} = -0.3m\). What is its half-life?
Q5: A 60°C object is placed in a 20°C room. After 10 minutes, the temperature of the object is 40°C. What is the temperature of the object after 20 minutes?
Q6: A box with a square base and an open top has a volume of \(32000\text{ cm}^3\). What dimensions of the box minimizes the materials used to make the box?
Q7: Find the dimensions of the largest rectangle that fits in between \(x^2\) and \(y=3\).
