SL 2.5—Modelling functions Questionbank

The number of bacteria in a Petri dish is modelled by the function $N(t)=75 \times 2^{0.5 t}, t \geq 0$ where $N$ is the number of bacteria and is the time in hours.

A hot winter soup has just been removed from the stove and is left outside to cool. The soup's temperature can be modelled by the function $T(t)=a+b\left(k^{-t}\right)$ where $t$ is the time, in minutes, since the soup was removed from the stove. The temperature outside is $12^{\circ} \mathrm{C}$.

Antibiotics $A$ and $B$ are applied to a pure culture of bacteria. The number of bacteria present initially for both antibiotics is 6000 . The number of bacteria present for antibiotic $A, N_{A}$, can be modelled by the function $N_{A}(t)=a \times b^{-t}, t \geq 0$ where $t$ is the elapsed time, in hours, since the start of the experiment.

In a biology lab, the population of a certain bacteria is observed to grow exponentially. The population ${P(t)}$ in number of bacteria at time ${t}$ hours is modeled by the equation:

${P(t) = 500e^{0.3t}}$

A company's profit per year was found to be changing at a rate of dP/dt = 3t² - 8t where P is the company's profit in thousands of dollars and t is the time since the company was founded, measured in years.

Consider the function f(x) = ax² + bx + c. The graph of y = f(x) is shown in the diagram. The vertex of the graph has coordinates (0.5, -12.5). The graph intersects the x-axis at two points, (-2, 0) and (p, 0).

Rosa joins a club to prepare to run a marathon. During the first training session Rosa runs a distance of 3000 metres. Each training session she increases the distance she runs by 400 metres.

A marathon is 42.195 kilometres.

In the $k$th training session Rosa will run further than a marathon for the first time.

Carlos joins the club to lose weight. He runs 7500 metres during the first month. The distance he runs increases by 20% each month.

The amount, in milligrams, of a medicinal drug in the body t hours after it was injected is given by D(t) = 23(0.85)^t, t ≥ 0. Before this injection, the amount of the drug in the body was zero.