The severity of rockbursts in a mine is measured on a local magnitude scale, with values usually ranging from $0$ to $4$, where $4$ represents the highest severity.

For one mining site, the annual number, $R$, of rockbursts reaching at least magnitude $m$ is modeled by ${\log }_{10}R=p-2m$, where $p\in \mathbb{R}$. At this site, there are on average $1000$ rockbursts per year with a magnitude of $1$ or greater.

The model is alternatively written as $R=\frac{d}{100^m}$.

The expected return period in years between rockbursts with magnitude at least $m$ is $\frac{1}{R}$.

The largest rockburst ever recorded at this site had magnitude $3.8$.

The area covered by an invasive plant in a pond is modelled by the function, $A(w)=c\times 2^w$, $w\ge 0$ where $c$ is a constant and $w$ represents the time in weeks since the beginning of the survey. It is observed that the area covered is 384 m${}^2$ after 6 weeks.

Give your answers to parts 1, 2 and 3 to the nearest whole number.

Elena has 16 000 euros (EUR) to invest for five years. She has two options for how to invest the money.

Option A: Invest the full amount, in EUR, in a fixed deposit account in a bank in Spain.

The account pays a nominal annual interest rate of k% , compounded yearly, for the five years. The bank manager says that this will give Elena a return of 19 654 EUR.

Option B: Invest the full amount, in Singapore dollars (SGD), in a fixed deposit account in a bank in Singapore. The money must be converted from EUR to SGD before it is invested.

The exchange rate is 1 EUR = 1.45 SGD.

The account in the bank in Singapore pays a nominal annual interest rate of 4.8 % compounded monthly.

Give your answers to parts 1, 2 and 3 to the nearest whole number.

Harinder has 14 000 US Dollars (USD) to invest for five years. He has two options of how to invest the money.

Option A: Invest the full amount, in USD, in a fixed deposit account in an American bank.

The account pays a nominal annual interest rate of r% , compounded yearly, for the five years. The bank manager says that this will give Harinder a return of 17 500 USD.

Option B: Invest the full amount, in Indian Rupees (INR), in a fixed deposit account in an Indian bank. The money must be converted from USD to INR before it is invested.

The exchange rate is 1 USD = 66.91 INR.

The account in the Indian bank pays a nominal annual interest rate of 5.2 % compounded monthly.

A candle maker uses a hemispherical mould to form a decorative candle. The mould has radius 9 cm and is filled exactly with molten wax. Before melting, the same wax was shaped as a right circular cone with base radius 7 cm.

After the filled mould is removed from a warming cabinet, the temperature, $W$, of the wax in degrees Celsius (°C), is modeled by the function:

$W(t)=a(1.28{)}^{-t}+22,t⩾0$

where $a$ is a constant and $t$ is the time in minutes after removal. The wax is initially at $150^{\circ }\text{C}$ and can be removed from the mould once it cools to $45^{\circ }\text{C}$.