Finansies: SREL-populasiegroei#2

'n Sekere bakterie verdubbel elke 25 minute.
As daar oorspronklik 1.6x10²³ was, hoeveel sal daar na 3 ure wees?

Bepaal eers die 'rentekoers' of populasie groei.

Gestel daar is oorspronklik 100 bakterieë en dit verdubbel na 200 in 25minute

$A equals 200 P equals 100 n equals fraction numerator 25 m i n u t e over denominator 60 end fraction equals 5 over 12 i equals ?$

$table attributes columnalign right center left columnspacing 0px end attributes row A equals cell P open parentheses 1 plus i close parentheses to the power of n end cell row 200 equals cell 100 open parentheses 1 plus i close parentheses to the power of 5 over 12 end exponent end cell row cell 200 over 100 end cell equals cell open parentheses 1 plus i close parentheses to the power of 5 over 12 end exponent end cell row 2 equals cell open parentheses 1 plus i close parentheses to the power of 5 over 12 end exponent end cell row cell root index 5 over 12 of 2 end cell equals cell 1 plus i end cell row cell 5.27803 end cell equals cell 1 plus i end cell row cell 5.27803 minus 1 end cell equals i row i equals cell 4.278... end cell end table$

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Gestel daar is oorspronklik x bakterieë en dit verdubbel na 2x in 25minute

$A equals 2 x P equals x n equals fraction numerator 25 m i n u t e over denominator 60 end fraction equals 5 over 12 i equals ?$

$table attributes columnalign right center left columnspacing 0px end attributes row A equals cell P open parentheses 1 plus i close parentheses to the power of n end cell row cell 2 x end cell equals cell 1 x open parentheses 1 plus i close parentheses to the power of 5 over 12 end exponent end cell row cell fraction numerator 2 up diagonal strike x over denominator 1 up diagonal strike x end fraction end cell equals cell open parentheses 1 plus i close parentheses to the power of 5 over 12 end exponent end cell row 2 equals cell open parentheses 1 plus i close parentheses to the power of 5 over 12 end exponent end cell row cell root index 5 over 12 of 2 end cell equals cell 1 plus i end cell row cell 5.27803 end cell equals cell 1 plus i end cell row cell 5.27803 minus 1 end cell equals i row i equals cell 4.278... end cell end table$

Bepaal nou die aantal bakterieë na 3 ure

$A equals ? P equals 1.6 x cross times 10 to the power of 23 n equals 3 i equals 4.278...$

$table attributes columnalign right center left columnspacing 0px end attributes row A equals cell P open parentheses 1 plus i close parentheses to the power of n end cell row blank equals cell 1.6 cross times 10 to the power of 23 open parentheses 1 plus 4.27803 close parentheses cubed end cell row blank equals cell 2.352 cross times 10 to the power of 25 end cell row blank equals cell 2.4 cross times 10 to the power of 25 end cell end table$