Question

The population of a particular type of bacteria is known to triple in 22 days. What is the daily growth rate

Answer 1

Answer: ∛(3)

Step-by-step explanation:

Suppose that at day 0 the population was A.

at day 3, the population will be: 3*A

at day 6, the population will be 3*(3*A) = A*3^2

then, at day N = 3*n (where n = 0, 1, 2.....) the population will be:

P(N) = A*3^n

Particularly, if we take n = 1/3 we will have:

N = 3*1/3 = 1

This means that this is the first day after the day 0.

P(1) = A*3^(1/3)

(then in day one, the population grow by a factor of 3^(1/3))

N = 2 is when n = 2/3, then:

P(2) = A*3^(2/3)

The quotient between P(2) and P(1) is equal to the growth between day one and day two, this should be the same as the growth between day zero and day one.

A*3^(2/3)/(A*3^(1/3)) = 3^( 2/3 - 1/3) = 3^(1/3)

So we found that the daily growth rate is 3^(1/3) or ∛(3)

Answer 2

The daily growth rate of the bacteria is an illustration of unit rates

The daily growth rate of the bacteria is 0.136

For 22 days, the population of the bacteria triples.

The daily rate is the amount of bacteria each day.

So, we have:

$\mathbf{Daily = \frac{Rate}{Days}}$

This gives

$\mathbf{Daily = \frac{3}{22}}$

Divide

$\mathbf{Daily = 0.136}$

Hence, the daily growing rate of the bacteria is 0.136

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