Exponential relations > Exponential growthExercises
The surface area covered by a fast growing water plant increases with 50% daily.
By what number should the surface area be multiplied if you want to know the area covered by plants tomorrow?
Does the covered surface area increase with 100% in two days? Or with another percentage? Explain.
Is this a case of exponential growth? Explain.
Somebody buys a quantity of shares worth euros. The value of the shares yearly increases with 11% during the first four years.
Calculate the value of the shares after one year and after two years.
What is the growth rate of the value of the shares per year?
How can you use the value after two years to calculate the value after three years?
After four years the value is € 6072.28. How can you use this number and the growth rate to calculate the value after three years?
During the sixth year the value of the shares rises from € 6740.23 to € 7279.45. With what percentage did the value increase? What is the new growth rate?
In a nature reserve there are deer in the year 2000. Counts have shown that this number decreases with 4% per year.
Make a formula for the 'growth' of the number of deer starting in the year 2000.
Calculate the number of deer in the year 2010.
In what year has the number of deer dropped to half the original number for the first time?
A sum of € 10000 is invested in shares for years. In the table you see the growth of the fortune in the first years.
| time in years | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| sum in euros | 10415 | 10850 | 11295 | 11760 | 12250 | 12750 | 13280 |
Show that the sum grows approximately exponentially in the first years.
The word "return" means the yearly growth of the invested amount expressed as a percentage.
Calculate the annual return for this period.
Make a table for a sum of € 10000 that is invested for years at an annual return of 8%.
After how many years has the fortune doubled?
Somebody invests a sum of € 10000 during years. Assume he gets an annual return of 14% during the first years and an annual return of 4% over the next years. Calculate the size of the sum after years and after years.
Use a calculation to show whether an investor earns more with respect to the previous situation if the annual return is 4% the first years and 14% the following years.
In two schools the number of students decreases:
| year (counting date 1 sep.) | 2005 | 2006 | 2007 | 2008 | 2009 |
| number of students school 1 | 1050 | 998 | 948 | 900 | 855 |
| number of students school 2 | 1050 | 1005 | 960 | 915 | 870 |
In one of the schools the number of students annually decreases with a fixed percentage. Which school and what percentage?
How does the decrease of the number of students in the other school behave?
School seems to end up with more students in the end. Is this true?
In this situation it is not relevant to look at smaller time steps than a year. Why not?