Model Exponential Growth Question :A sample of bacteria is growing at a continuously compounding rate. The sample triples in 10

Question

3 months ago

9

days Find the formula for the daily rate. Type your answer as a fraction.

1 answer:

Inessa [12.5K] · Answer 1 · 2026-03-04T16:00:36+03:00

Answer:

The bacteria count $B$ after $d$ days is represented by

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

where $B_0$ indicates the starting amount of bacteria.

Step-by-step explanation:

In the sample, the bacterial population triples every 10 days, which implies that at the completion of the first 10 days, the bacterial count reaches

$B = B_0 *3,$

where $B_0$ denotes the original count of bacteria in the sample.

Following the second set of 10 days, the bacterial count becomes

$B = (B_0 *3)*3$

after the third set of days,

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

and this pattern continues.

This leads us to the formula for the bacterial population after the nth period of 10 days, expressed as

$B = B_0 (3)^n$

where $n$ signifies the nth 10-day segment.

Since $n$ equals 10 days, we arrive at

$d =10n$

which simplifies to

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

By substituting this back into $B = B_0 (3)^n$ , we find:

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