The document discusses cooling of hot chocolate over time. It provides an initial temperature of 98°C and asks what the temperature will be after 3 minutes, given it is 38°C after 5 minutes. It uses an exponential cooling formula and graphs the temperature changes from 0-7 minutes. The temperature after 3 minutes is around 52°C. It also answers additional questions about when the temperature would reach 3°C and what it would be after 7 minutes.

1. PRIMJENA
EKSPONENCIJONALNE
FUNKCIJE
APPLICATION OF
EXPONENTIAL
FUNCTION
HLAĐENJE TOPLE ČOKOLADE
COOLING OF HOT CHOCOLATE
Lucija Barčić, SŠ Markantuna de
Dominisa Rab, 7.12.2020

2. ZADATAK/ TASK
Nedavno u RH zbog korone epidemiološke mjere su
se znanatno postrožile te je zabranjen rad kafića. Na
svu sreću, kafići su omogućili opciju take-away te je
grupa prijatelja odlučila kupiti toplu čokoladu
početne temperature 98 °C. Hodajući gradom pri
temperaturi zraka 18°C kolika će biti temperatura
tople čokolade nakon 3 minute, ako nakon 5 minuta
iznosi 38°C?
Recently in the Republic of Croatia, due to the
corona, epidemiological measures have become
significantly stricter and the operation of cafes has
been banned. Fortunately, the cafes provided a take-
away option and a group of friends decided to buy
hot chocolate with an initial temperature of 98 ° C.
Walking through the city at an air temperature of 18
° C, what will be the temperature of hot chocolate
after 3 minutes, if after 5 minutes it is 38 ° C?

3. FORMULA FUNKCIJE/ FUNCTION FORMULA
Za računanje ovog zadatka potrebno je koristiti Newtonov zakon
hlađenja:
To calculate this task it is necessary to use Newton's law of cooling:

4. GRAF FUNKCIJE/ GRAPH
t (u minutama) T (temp. napitka u °C
0 98
1 78.63
2 63.94
3 52.82
4 44.39
5 38
6 33.15
Time in minutes temperature of
hot chocolate in
°C

5. • Temperatura tople čokolade
eksponencijonalno pada s
vremenom
• Iz grafa možemo očitati da
temperatura tople čokolade će
nakon 3 minute biti oko 52 °C
• The temperature of hot chocolate
drops exponentially with time
• From the graph we can read that
the temperature of the hot
chocolate will be around 52 ° C
after 3 minutes

6. KOLIKA ĆE BITI TEMPERATURA TOPLE ČOKOLADE
NAKON 7 MINUTA?
WHAT WILL BE THE TEMPERATURE OF HOT
CHOCOLATE AFTER 7 MINUTES?
Nakon 7 minuta temperatura tople
čokolade će biti oko 29 °C
After 7 minutes the temperature of
the hot chocolate will be around 29
° C

7. KADA ĆE TEMPERATURA TOPLE ČOKOLADE BITI
PRIBLIŽNA 3 °C?
WHEN WILL THE TEMPERATURE OF HOT
CHOCOLATE BE APPROXIMATE TO 3 ° C?
Logaritam od negativnog broja ne postoji,
temperatura tople čokolade nikada neće
biti približna 3 °C
To možemo i očitati s grafa.
There is no logarithm of a negative
number, the temperature of hot
chocolate will never be close to 3 ° C
We can also read this from the graph.

8. KOLIKA ĆE TEMPERATURA TOPLE
ČOKOLADE BITI ZA 3 MINUTE?
HOW MUCH WILL THE CHOCOLATE
TEMPERATURE BE IN 3 MINUTES?
Temperatura tople čokolade za 3
minute će biti oko 52 °C
The temperature of the hot chocolate
in 3 minutes will be around 52 ° C

9. Ideju za pp sam dobila od yt videa o hlađenju čaja te
sam se prisjetila odlaska na toplu čokoladu s
prijateljima i čekanja da se čokolada ohladi.
https://hrcak.srce.hr/file/166771
https://youtu.be/ISuRUMflT1g
HVALA NA PAŽNJI!
THANK YOU FOR
ATTENTION!
I got the idea for pp from a yt video about cooling
tea and I remembered going for hot chocolate
with friends and waiting for the chocolate to cool.