Question

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.

Answer 1

`d=6+Log_(10)16^2`

Explanation:

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

`B=50*10^{d/2`

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

`800000=50*10^(d/2)\\$Divide both sides by 50\\16000=10^(d/2)\\$Convert to logarithm form\\Log_(10)16000=(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`