Model Exponential Growth Question :A sample of bacteria is growing at a continuously compounding rate. The sample triples in 10 days Find the formula for the daily rate. Type your answer as a fraction.

The daily rate of the bacteria growth is

An exponential growth is in the form:

y = abˣ;

where y, x are variables, a is the initial value of y and b > 1

Let y represent the number of bacteria after x days.

The sample triples in 10 days. hence:

b = 3

The equation becomes:

Therefore the daily rate is

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The number of bacteria after days is given by

where is the initial number of bacteria.  

Step-by-step explanation:

The number of bacteria in the sample triples every 10 days, this means after the first 10th day, the number of bacteria is

where is the initial number of bacteria in the sample.

After the 2nd 10th days, the number of bacteria is

after the 3rd day,

and so on.

Thus, the formula we get for the number of bacteria after the nth 10-days is

where is is the nth 10-days.

Since, is 10 days, we have

or

Substituting that into , we get:

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step-by-step explanation: