1 Answer

Tomislav Stankovic · Answer 1 · 2023-02-17T10:15:53+0000

Given data:

The given growth rate is r=7.8%=0.078.

The final number of bacteias in terms of initial is P'=2P.

The expression for the bacterias growth rate is,

$P^(\prime)=P(1+r)^t$

Substitute the given values in the above expression.

$\begin{gathered} 2P=P(1+0.078)^t \\ 2=(1.078)^t \\ \ln (2)=t\ln (1.078) \\ t=(\ln(2))/(\ln(1.078)) \\ =9.23\text{ hours} \end{gathered}$

Thus, after 9.23 hours population of the bacterias doubled.

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