Question

A scientist writes the equation n(h)100e^0.25h to model the growth of a certain bacteria in a petri dish, where N represents the number of bacteria after h hours. After approximately how many hours will 450 bacteria be present? Round your answer to the nearest whole number.

1 hour
6 hours
13 hours
15 hours

Answer 1

6 hours is the amount of time

Answer 2

Answer: Second option is correct.

Explanation:

Since we have given that

`n(h)=100e^(0.25h)`

where, N represents the number of bacteria after 'h' hours.

So, we have given that there are 450 bacteria present.

N = 450

According to question,

`450=100e^(0.25h)\\\\(450)/(100)=e^(0.25h)\\\\4.5=e^(0.25h)\\\\\text{Taking natural log 'ln' on both sides}\\\\\ln (4.5)=0.25h\\\\1.50=0.25h\\\\h=(1.50)/(0.25)\\\\h\approx 6\ hours`

Hence, Second option is correct.