.1. Exercise:
Grandpa has 1000.- in his piggy bank. Every year he adds 90.- to it.
Grandma has a savings book with 1000.- credit. She receives 5% interest per year on this credit, but does not make any deposits.
a) How much money does Grandpa have after 8 years?
b) After how many years does he have more than 2000.-?
c) Design a semantic model and present Grandpa's assets as a function of time as a graph and table. Read from it the solutions of a) and b). .
d) Now design a semnatic model for the development of Grandma's assets and present it in a table and graph.
e) How big is her credit balance after 8 years?
f) After how many years does her credit exceed 2000.-?
g) Is it possible that Grandma has a larger credit balance than Grandpa, although she never saves?
h) Draw up a graphic model for both types of growth. What is characteristic of linear or exponential growth?
Describe the difference between these types of growth in the linguistic, graphical and algorithmic model.
2. Exercise:
Nancy is 16 years old. Until her 18th birthday in 24 months she receives 50.- pocket money per month. Since she has learned about the advantages of exponential growth, she proposes the following new pocket money model to her parents:
She receives one cent pocket money in the first month. In each following month she will always receive twice as much pocket money as in the previous month. Which model is cheaper for Nancy?
3. Exercise:
In a radioactive compound, 5% of the existing atoms decay every second. How many % of the atoms decay in a minute, an hour, a year?
After which time are only half of the atoms left (half-life)?