Functions Questionbank

A particle moves along a straight line with displacement, $s(t)$, in meters, from a fixed point at time $t$ seconds, modeled by

for $0 \leq t \leq 30$. The particle is at risk of collision when $|s(t)| \geq 6$.

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 $12^{\circ} \mathrm{C}$.

The point $A(-1,3)$ lies on the curve $y=f(x)$.

The front view of the edge of a water tank is drawn on a set of axes below. The edge is modelled by $y=a x^{2}+c$

Point $P$ has coordinates $(-4,4)$, point $O$ has coordinates $(0,0)$ and point $Q$ has coordinates $(4,4)$.

The point $A(1,0.5)$ lies on the curve $y=f(x)$. Write down the coordinates of the corresponding point under the following transformations.

The average temperature of a city, $C$, in degrees Celsius, fluctuates throughout a year and can be modelled by the function $C(t)=a \sin (k t)+b$ where $t$ is the elapsed time, in weeks, since the start of the year. The average temperature of the city in week 4 is 27 degrees Celsius and in week 28 it is 12 degrees Celsius.

A geologist models the decay of seismic wave amplitude $A$ with distance $d$ (in km) from an earthquake epicenter, using $A=k d^{n} e^{m d}$, where $k, n, m$ are constants. Data is plotted as $\ln A$ against $\ln d$, but due to the exponential term, the graph is not perfectly linear. However, for small $d$, the term $e^{m d} \approx 1$, and the plot approximates a straight line through $(0,5)$ and $(1,2)$.

Graph of $\ln A$ against $\ln d$

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.

A chemist studies the rate $R$ of a reaction as a function of concentrations $A$ and $B$ of two reactants, modeled by $R=k A^{x} B^{y}$. The following data is collected: