The population of bacteria in a petri dish doubles every 24 h. The population of the bacteria is initially 500 organisms. How long will it take for the population of the bacteri…

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asked Jul 6, 2019 146k views

1 Answer

Naoto Usuyama · Answer 1 · 2019-07-10T04:02:58+0000

Answer:

C. 16.3

Explanation:

The function for exponential growth is,

y(t)=Ae^(rt)

where,

y(t) = the future amount,

A = initial amount,

r = rate of growth,

t = time.

As the population of bacteria in a Petri dish doubles every 24 h, so

$\Rightarrow 2A=Ae^(r* 24)$

$\Rightarrow 2=e^(r* 24)$

$\Rightarrow \ln 2=\ln e^(r* 24)$

$\Rightarrow \ln 2={r* 24}* \ln e$

$\Rightarrow \ln 2={r* 24}* 1$

$\Rightarrow r* 24=\ln 2$

$\Rightarrow r=(\ln 2)/(24)$

The population of the bacteria is initially 500 organisms, so the function becomes,

$y(t)=500e^{(\ln 2)/(24)* t}$

We have to calculate t, when the the population of bacteria becomes 800. So,

$\Rightarrow 800=500e^{(\ln 2)/(24)* t}$

$\Rightarrow (800)/(500)=e^{(\ln 2)/(24)* t}$

$\Rightarrow \ln (800)/(500)=\ln e^{(\ln 2)/(24)* t}$

$\Rightarrow \ln 1.6={(\ln 2)/(24)* t}* \ln e$

$\Rightarrow \ln 1.6={(\ln 2)/(24)* t}* 1$

$\Rightarrow \ln 1.6={(\ln 2)/(24)* t$

$\Rightarrow t=(\ln 1.6)/((\ln 2)/(24))$

$\Rightarrow t=16.3\ h$