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The relationship between B, the number of bacteria in the culture, and d, the elapsed time, in days, is modeled by the following equation.
B=50*10^d/2
In how many days will the number of bacteria in the culture reach 800,000?
Give an exact answer expressed as a base-ten logarithm.

Respuesta :

Answer:

[tex]d=6+Log_{10}16^2[/tex]

Step-by-step explanation:

The number of bacteria in the culture is represented by the model:

[tex]B=50*10^{d/2[/tex]

We are required to find the number of days, d when the number of bacteria is 800,000. Therefore:

[tex]800000=50*10^{d/2}\\$Divide both sides by 50\\16000=10^{d/2}\\$Convert to logarithm form\\Log_{10}16000=\frac{d}{2}\\ $Cross Multiply\\d=2Log_{10}16000\\=2[Log_{10}(16X1000)]\\=2Log_{10}16+2Log_{10}(1000}\\=2Log_{10}16}+6\\d=6+Log_{10}16^2[/tex]