Question

Following the 1989 Exxon Valdez oil spill, 100 km of the Arctic shoreline was contaminated. Crude oil is made up of thousands of compounds. It takes many different kinds of naturally occurring bacteria to break the oil down. Lab technicians identified and counted the bacteria. They monitored how well the oil was degrading. More bacteria and less oil were signs that the shoreline was recovering. The number of bacteria needed to effectively break down an oil spill is 1,000,000 per milliliter of oil. The bacteria double in number every 2 days. The starting concentration of bacteria is 1000 bacteria per milliliter. This situation can be modeled by the equation C= 1000(2)d, where C is the estimated concentration of bacteria and 'd' is the number of 2-day periods the bacteria grow.

Approximately how long would it take for the bacteria to reach the required concentration to break down 1 mL of oil?

Answer 1

The bacteria would take approximately 19.932 days to reach the required concentration to break down 1 mL of oil.

Step-by-step explanation:

The situation described can be modeled by the equation C= 1000(2)d, where C is the estimated concentration of bacteria and 'd' is the number of 2-day periods the bacteria grow. To find the number of 2-day periods it would take for the bacteria to reach the required concentration of 1,000,000 per milliliter of oil, we can set up the equation:

1,000,000 = 1000(2)d

To solve for 'd', we need to find the exponent that gives us a result of 1,000,000. We can rewrite the equation in exponential form and solve for 'd':

2d = 1000

d = log2(1000)

Using a calculator, we find that d is approximately 9.966. Therefore, it would take approximately 9.966 × 2 = 19.932 days for the bacteria to reach the required concentration to break down 1 mL of oil.