Question

In a lab experiment, 50 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 16 hours. How long would it be, to the nearest tenth of an hour, until there are 170 bacteria present?

Answer 1

Answer:

time = 28.25 hours

Step-by-step explanation:

given data

petri dish = 50 bacteria

number of bacteria double =  every 16 hours

bacteria present = 170

solution

we know equation of  population of bacteria is

$P = P_0 e^{rt}$      .........................1

and we know after 16 hour bacteria is able to double

so

P = 2 $P_0$  

when we apply this we get

$2P_0 = P_0e^{16r}$

$2=e^{16r}$

take ln both side we get

ln(2)  = 16 r  

r =  $\frac{ ln(2) }{16}$

r = 0.04332

so when here 170 bacteria present

than it will take time

170 = $50e^{0.04332t}$

take ln both side

$ln( \frac{170}{50}) = 0.04332t$

1.2237 = 0.04332t

t = 28.25 hours