## A piece of chicken contains approximately 1 billion live salmonella. Cooking it on low heat for 4 minutes kills 90% of those bacteria. how long would you have to cook it to reduce the bacterial count to 1000 bacteria.

### 24 minutes

To answer this question, we can first calculate how many bacteria will remain after cooking the chicken for four minutes and reducing the count by 90%.

90% of 1 billion bacteria will be killed, leaving 10% of the original bacteria to remain.

So,

1 billion x 0.1 = 100 million live bacteria remaining after cooking for four minutes.

Now we can calculate the time needed to further reduce the bacterial count from 100 million to 1000.

To do this, we can use the formula:

Nt = N0 x 2^(-t/h)

where:

Nt is the final number of bacteria

N0 is the initial number of bacteria

t is the time

h is the time it takes for the bacteria count to reduce by half (also known as the “half-life” of the bacteria)

In our case, we want to reduce the bacteria count from 100 million to 1000, which is a 100,000-fold reduction. Therefore, we can substitute the values into the formula:

1000 = 1 x 10^8 x 2^(-t/h)

Taking the logarithm of both sides, we get:

log(1000) = log(1 x 10^8) + log(2) x (-t/h)

3 = 8 + (-t/h) x 0.301

(-t/h) = (3 – 8) / 0.301 = -16.6

t = (-16.6) x h

The time required to reduce the bacterial count to 1000 can then be calculated as follows:

t = (-16.6) x 4 = -66.4 minutes

Since we cannot have negative time, we can round up to the nearest integer, which gives us:

t = 67 minutes

Therefore, the chicken would need to be cooked for approximately 67 minutes on low heat to reduce the bacterial count from 1 billion to 1000.

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