Question

A culture of bacteria starts with 50 bacteria and increases exponentially.

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
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

To find the number of days it will take for the number of bacteria in the culture to reach 800,000, we can use the exponential growth equation B = 50 x 2^(d/10), where B is the number of bacteria and d is the elapsed time in days. Plugging in B = 800,000, we can calculate d using logarithm properties. By rearranging the equation and solving for d, we find that it will take approximately 16.6437 days for the number of bacteria to reach 800,000.

Step-by-step explanation:

To find the number of days it will take for the number of bacteria in the culture to reach 800,000, we can use the exponential growth equation B = 50 x 2^(d/10), where B is the number of bacteria and d is the elapsed time in days. We can rearrange the equation to solve for d as follows:

d = 10 x log2(B/50)

Plugging in B = 800,000, we can calculate d using logarithm properties:

d = 10 x log2(800,000/50)

Using a calculator, we find that d ≈ 16.6437 days. Therefore, it will take approximately 16.6437 days for the number of bacteria in the culture to reach 800,000.

Answer 2

2log(16000)

Step-by-step explanation: