Exponential functions

Exponential functions > Exponential growth

12345Exponential growth

Exercises

Exercise 1

In a shallow lake with a surface area of more than $1000$ km² cane starts growing. On 1-1-1995 the area of the cane-covered part is $2$ 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 $R (t)$ , where $t$ 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?

Exercise 2

Write as one power:

$2^{4} \cdot 2^{3}$

${(2^{3})}^{2} \cdot 2^{4} + 2^{3} \cdot 2^{7}$

$\frac{2^{512}}{2^{509}}$

${(2^{53})}^{3} \cdot {(\frac{1}{2})}^{100}$

Exercise 3

In a certain nature reserve there are $5000$ 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?

Exercise 4

Write as one power:

$\frac{3^{214}}{3^{211}}$

$3^{110} \cdot {(\frac{1}{3})}^{109}$

$\frac{{(3^{16})}^{10}}{3^{100} \cdot 3^{60}}$

${(\frac{3}{4})}^{235} \cdot {(\frac{4}{3})}^{236}$

Exercise 5

A sum of € 10000 is invested in shares for $10$ years. In the table you see the growth of the sum in the first $6$ 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 $6$ 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 $10$ years. Assume he gets an annual return of 14% for the first $5$ years and an annual return of 4% the next $5$ years. Calculate the size of the sum $K$ after $5$ years and after $10$ 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 $5$ years and 14% the next 5 years.

previous | next