Ascientist is testing a new antibiotic by applying the antibiotic to a colony of 10,000 bacteria. the number of bacteria decreases by 75% every two hours. how many hours will it take for the bacteria colony to decrease to 1000? round your answer to the nearest tenth of an hour.

3.3 hours.

Step-by-step explanation:

We have been given that a scientist is testing a new antibiotic by applying the antibiotic to a colony of 10,000 bacteria. The number of bacteria decreases by 75% every two hours.

Since number of bacteria is decreasing exponentially, so we will use exponential decay function.

, where,

a= Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

As number of bacteria is decreasing every 2 hours, so number of bacteria decreased in 1 hour will be x/2.

Upon substituting our given values in above formula we will get,

To find the number of hours it will take to for the bacteria colony to decrease to 1000, we will substitute y = 1,000 in our equation.

Let us divide both sides of our equation by 10,000.

Let us take natural log of both sides of our equation.

Therefore, it will take 3.3 hours  for the bacteria colony to decrease to 1000.

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step-by-step explanation: