IB DP Computer Science Option B: Modelling and simulation -: B.2 – Simulations SL Paper 2

Question

Global warming is a term used to describe the increase in mean global temperatures.
There have been numerous computer simulations developed to predict the effects of global warming. One simulation is NASA’s Virtual Earth System Laboratory (VESL), which allows users to see how climate change affects glacier size, global sea level and changes to the coastline.
The VESL runs simulations in real time and is an abstraction of reality.
A recent study reported that previous simulations of predicted global sea levels for 2100 were highly inaccurate.
a.i. Outline what is meant by a real-time simulation in the context of a glacier size simulation.[2]
a.ii.Outline what is meant by the statement “the VESL simulation is an abstraction of reality”.[2]
b. Outline two reasons why predictions of global sea levels from simulations may not be accurate.[4]
c. NASA has decided to make its simulation software available for other scientists as well as members of the public. [6]
Evaluate the social and ethical implications of this decision.

▶️Answer/Explanation

Ans:

a.i. )
A real-time simulation runs at the same rate as the actual physical system;
The change in the glacier size occurs at the same rate as the real change / a virtual glacier will be the same size as the real glacier after the same period of time;
A real time simulation operations it can mean that it happens without a delay/action carried out before the next input; Changes to the simulation inputs will be displayed immediately;

a.ii )
Abstraction removes specific detail that will not the accuracy of the simulation / climate change variables that have little influence;
Abstractions helps create the model / reduces the complexity of the model so that it works effectively;
Symbols may be used to represent patterns (e.g. temperature change);

b. )
Sea levels are based on so many factors (e.g. $\mathrm{CO}_2$ emissions, cattle); that it is difficult to accurate predict all of these variables;
Global events (eg nuclear war, volcanic eruptions);
may cause for an under-prediction;
Unknown variables (confounding factors) may be affecting rising sea levels;
Population growth may increase or decrease and this may impact upon emissions;
Accept any reasonable argument
c. Award $[6 \max ]$.
Award [3 max] for positive reasons.
Award [3 max] for negative reasons.
Award [1 max] for a reasonable conclusion.

c. )
Award $[3 \max ]$ for positive reasons.
Award [3 max] for negative reasons.
Award [1 max] for a reasonable conclusion.
Positive
Making it free means more people may use it;
Educating the public may encourage more people to be environmental friendly (e.g. boycott plastics);
This may lead to pressure on governments to reduce emissions;
May provide valuable data for scientists who don’t have access to NASA resources;
Negative
Users may not fully understand the simulation results and may misinterpret findings;
May change the perception of the accuracy of the simulation software / Users may not value predictions when the simulator seems so simple; Predictions that don’t reflect the real change may do damage to public perception of climate change;

Question

Investment planning is something that many people need to be aware of. Planning for your future requires research because bad choices can be very costly.
Interest paid on money invested is usually in the form of compound interest. The formula to calculate compound interest is:

$
\mathrm{T}=\mathrm{P} *(1+\mathrm{r})^{\mathrm{n}}
$

$\mathbf{T}$ is the total value of the investment,
$\mathbf{P}$ is the principal sum invested,
$\mathbf{r}$ is the interest rate per time period converted to a decimal (for example, $5 \%$ is 0.05),
$\mathbf{n}$ is the number of time periods.
An additional $\$ 1000$ is added to a principal amount of $\$ 30000$ at the end of each month.
The monthly interest rate is $0.5 \%$ and this rate is compounded at the end of each month.

An additional $\$ 1000$ is added to a principal amount of $\$ 30000$ at the end of each month.
The monthly interest rate is $0.5 \%$ and this rate is compounded at the end of each month.
Each month, tax is calculated on the monthly profit at a rate of $25 \%$ when the investment total $(T)$ is $\$ 40000$, or below. However, when the investment total $(T)$ is above $\$ 40000$, the tax rate is $40 \%$.

The tax is calculated at the end of each month after interest has been added. A running total of the tax is kept and only deducted from the investment total $(T)$ at the end of the year.
a. Calculate the total value of the investment after two years if the principal sum of $\$ 30000$ is invested. The yearly interest rate is $10 \%$ and this rate [2]

is compounded at the end of each year.
b. Outline, using a diagram or otherwise, a method of calculating the total value of the investment after 12 months.[5]
c. Construct an algorithm to calculate the fund value at the end of each month. This algorithm should also calculate the total value of the investment [6]

after the tax has been deducted after 12months.
d. Many investment companies offer alternative investment schemes and use modelling to set the rates of interest.[4]
Explain why the investment company would use modelling when setting the rates of interest.

▶️Answer/Explanation

Ans:

a.)
                              $
                              36300
                                 $
if interest only award [1 mark max], $\$ 6300$;

b. )
Award [1] Initial investment 30000 for month 0;
Award [1] Investment 1000 each month;
Award [1] Interest rate of 0.005 * Principal
Award [1] Calculate compound interest for 12 months;
Award [1] Add interest to the investment;

c. )
An array does not need to be used to obtain full marks.
Award [1] Create array or variables / initialise array or variables $/ P[0]=30000$;
Award [1] Create interest rate and assign it to 1.005 ;
Award [1] Calculate interest;
Award [1] Add interest and 1000 to each month;
Award [1] If statement to determine the correct tax rate;
Award [1] Output investment – tax;

\begin{aligned}
& \mathrm{P}[0: 12]=0 \\
& \mathrm{P}[0]=30000 \\
& \text { RATE }=1+0.005 \\
& \text { TAX }=0 \\
& \text { Loop } X \text { from } 0 \text { to } 11 \\
& \text { INVESTMENT }=\mathrm{P}[\mathrm{X}]{ }^* \text { RATE } \\
& \quad \mathrm{P}[\mathrm{X}+1]=1000+\mathrm{INVESTMENT} \\
& \quad \text { PROFIT }=\text { INVESTMENT }-\mathrm{P}[\mathrm{X}] \\
& \text { If } \mathrm{P}[\mathrm{X}+1]<40000 \text { then } \\
& \text { TAX }=\text { TAX }+\left(\text { PROFIT }{ }^* 0.25\right) \\
& \text { Else } \\
& \text { TAX }=\text { TAX }+\left(\text { PROFIT }{ }^* 0.40\right) \\
& \text { End if } \\
& \text { End Loop } \\
& \text { Output (“Investment Value: }{ }^*,{ }^* \mathrm{P}[12]-\text { TAX) }
\end{aligned}

Alternative solution without an array

PRINCIPAL $=30000$
RATE $=1+0.005$
$\mathrm{TAX}=0$
Loop $X$ from 0 to 11
OLD_PRINCIPAL $=$ PRINCIPAL
INVESTMENT $=$ OLD_PRINCIPAL * RATE
PRINCIPAL $=1000+$ INVESTMENT
PROFIT = INVESTMENT – OLD_PRINCIPAL
if PRINCIPAL $<=40000$ :
$\mathrm{TAX}=\mathrm{TAX}+\left(\mathrm{PROFIT}^* 0.25\right)$ else:
$\mathrm{TAX}=\mathrm{TAX}+\left(\mathrm{PROFIT}^* 0.40\right)$ end if
End Loop
Output (“Investment Value: “, PRINCIPAL – TAX)

d. )
A what if scenario can be employed;
A mathematical model will allow you to adjust variables to see what impact that will have on the investment;
You can see exactly what is happening to the money each month;
If the client decides to pay in less or more money for a given month you can see what affect this will have on the profits;
If the interest rate changes, you will be able to see what changes this has on profit;
If the tax rate changes you can see how this affects the investment profits.

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