Question

Can someone please help me with this math, thank you

Answer 1

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.