Question

A sample of bacteria is growing at a continuously compounding rate. The sample triples in 10 days.

Answer 1

Answer:

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