Question

In a lab experiment, 100 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 13 hours. How long would it be, to
the nearest tenth of an hour, until there are 156 bacteria present?

Answer 1

Answer: 8.34 hr

Step-by-step explanation:

Given

Initially, 100 bacteria are placed in a Petri dish

bacteria doubles in every 13 hours

So, a function that defines this relation is given as

$\Rightarrow B=B_o(2)^\frac{t}{13}$

where, $B=\text{No of bacteria at any time}$

$B_o=\text{Intial bacterias}\\t=\text{time in hrs}$

for $B=156$

$\Rightarrow 156=100\times 2^{\frac{t}{13}}\\\\\Rightarrow 1.56=2^{\frac{t}{13}}\\\\\Rightarrow t=13\times \dfrac{\ln (1.56)}{\ln (2)}\\\\\Rightarrow t=13\times0.641=8.34\ hr$