Question

A culture of bacteria has an initial population of 41000 bacteria and doubles every 5 hours. Using the formula P t = P 0 ⋅ 2 t d P t ​ =P 0 ​ ⋅2 d t ​ , where P t P t ​ is the population after t hours, P 0 P 0 ​ is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 14 hours, to the nearest whole number?

Answer 1

285541.

Explanation:

P0=41000-The initial population

t=14-Time elapsed

d=5-The doubling time

Pt=P0⋅2^t/d

Pt=41000⋅2^14/5-Plug in

Pt=285540.5848≈285541-(Use parenthesis in the calculator for the exponent)

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Answer 2

Population of bacteria in culture after 14 hours is 285541.

Explanation:

We are given with
`P_(t) =P_(0)(2)^{(d)/(t)}`

Here initial population is 41000 , t=5 and d=14

Plug in these values into the formula

`P_(14) =41000(2)^{(14)/(5) }`

Simplify

`P_(14)= 41000(2)^(2.8)`

=41000(6.9644)

=285540.5847...

To the nearest whole number is 285541.