In a shallow lake with a surface area of more than km2 cane starts growing. On 1-1-1995 the area of the cane-covered part is km2.
From that moment on the cane-covered area is measured.
In 1998 it is established that the cane-covered area has tripled yearly sinds the
start of the measurements. Assume that the cane continues to expand like this.
Give the formula for the cane covered area , where is the time in years.
Use this formula to make a table for the first five years.
After how many years is the lake completely covered by the cane?
Write as one power:
In a certain nature reserve there are deer in the year 2000. Observations 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.
Calculate the growth rate for a time step of 10 years.
In what year has the number of deer dropped to half the original number for the first time?
Write as one power:
A sum of € 10000 is invested in shares for years. In the table you see the growth of the sum in the first years.
time in years | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
sum in euros | 10415 | 10850 | 11295 | 11760 | 12250 | 12750 | 13280 |
The word "return" means the yearly growth of the invested amount expressed as a percentage.
Show that the fortune grows approximately exponentially in the first years.
Calculate the annual return for this period.
Make a table for a sum of € 10000 that is invested for 10 years at an annual return of 8% .
After how many years has the sum doubled?
Somebody invests a sum of € 10000 during years. Assume he gets an annual return of 14% for the first years and an annual return of 4% 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 next 5 years.