Question

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.

Answer 1

Answer:

The number of bacteria $B$ after $d$ days is given by

$B = B_0 (3)^{\frac{1}{10} d}$

where $B_0$ is the initial number of bacteria.  

Step-by-step explanation:

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

$B = B_0 *3,$

where $B_0$ is the initial number of bacteria in the sample.

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

$B = (B_0 *3)*3$

after the 3rd day,

$B =( B_0 *3*3)*3$

and so on.

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

$B = B_0 (3)^n$

where $n$ is is the nth 10-days.

Since, $n$ is 10 days, we have

$d =10n$

or

$n =\dfrac{1}{10}$

Substituting that into $B = B_0 (3)^n$, we get:

$\boxed{ B = B_0 (3)^{\frac{1}{10} d}}$