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There are 100 bacteria in a jar. Every day, the number of bacteria increases 25%. In approximately how many days will there be 500 bactria in the jar? Pick the closest answer.
A. 3
B. 12
C. 10
D. 2
E. 7

Respuesta :

semsee45

Answer:

E. 7

Step-by-step explanation:

General form of exponential equation:  [tex]y=ab^x[/tex]

where [tex]a[/tex] is the initial value, [tex]b[/tex] is the growth/decay rate, and [tex]x[/tex] is time.

Given:

  • [tex]a[/tex] = 100 bacteria
  • [tex]b[/tex] = 25% increase = 1.25
  • [tex]x[/tex] = number of days

⇒ [tex]y=100 \cdot 1.25^x[/tex]

If y = 500, then:

[tex]\implies 500=100 \cdot 1.25^x[/tex]

[tex]\implies 5=1.25^x[/tex]

[tex]\implies \ln5=\ln1.25^x[/tex]

[tex]\implies \ln5=x\ln1.25^[/tex]

[tex]\implies x=\dfrac{\ln5}{\ln1.25}[/tex]

[tex]\implies x=7.212567439...[/tex]

[tex]\implies x \approx7[/tex]

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