Question

The bacteria in a Petri dish culture are self-duplicating at a rapid pace.

The relationship between the elapsed time ttt, in minutes, and the number of bacteria, B(t)B(t)B, left parenthesis, t, right parenthesis, in the Petri dish is modeled by the following function.

B(t)=100⋅2t10

How many minutes will it take for the culture to achieve 10{,}00010,00010, comma, 000 bacteria?
Round your answer, if necessary, to the nearest hundredth.

Answer 1

10,240

Explanation:

It showed it as the right answer on khan academy

Answer 2

66.44 Minutes

Explanation:

The number of Bacteria, B(t) at any time t(in minutes) is given by the function:

`B(t)=100\cdot 2^(t/10)`

We want to determine the time(in minutes) for the culture to achieve 10,000 bacteria.

Therefore:

`10000=100\cdot 2^(t/10)`

Divide both sides by 100

`100=2^(t/10)\\$Change to logarithm form\\Log_(2)100=t/10\\(Log 100)/(Log 2)= (t)/(10)\\t=10*(Log 100)/(Log 2)\\t=66.44 $ minutes (correct to the nearest hundredth)`