Exponential relations

Exponential relations > Calculations with powers

1234Calculations with powers

Exercises

Exercise 1

In a shallow lake with a surface area of $1000$ km² cane starts growing. On 1 January 2005 the area of the lake covered by cane is $1$ km².
From then on the area of the cane covered part is measured regularly.
In 2010 it is established that the area of the cane covered part has doubled every year. Assume that the cane continues to expand at the same rate.

What is the yearly growth rate?

Make a table for the cane covered area for the first five years.

What is the growth rate per ten years?

After how many years is the lake fully covered by 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

The concentration of a certain pollutant in the water decreases slowly with a percentage of 13% per hour. At $t = 0$ the concentration is $150$ mg per liter.

What is the growth rate per hour? Construct a formula for the concentration $C$ depending on time $t$ in hours.

After how many hours has the concentration halved?

With what percentage does the concentration diminish per day?

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

Somebody buys shares worth € 5000. In the following months the value of the shares decays exponentially. After one month the value of the shares has diminished with € 600.

How many percent is $600$ of 5000?

Calculate the growth rate of the value of the shares.

Make a table with the value of the shares for the first five months.

By what number do you have to multiply the value after five months to get the value after ten months? Compute the value after ten months.

What is the growth rate per ten months? And per fifteen months?

In how many months does the value of the shares halve?

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