Question

11. A bacteria colony started with 2 bacteria. The colony is growing exponentially at 10%per hour. How long will it take to have 1 million bacteria?(Exponential Growth/Decay)

Answer 1

1319 hours

Step-by-step explanation

We have that the bacteria colony started with just 2 bacteria.

The colony is growing exponentially. The rate is 10% or 0.01.

The formula for amount of an exponential growth is:

`\begin{gathered} A=a(1+r)^t \\ t\text{ = time in hours} \\ r\text{ = rate = 0.01} \\ a\text{ = intial amount of bacteria = 2} \end{gathered}`

Therefore, we have that:

`\begin{gathered} 1000000=2(1+0.01)^t \\ (1000000)/(2)=1.01^t \\ \Rightarrow500000=1.01^t \\ \text{Convert this to logarithm, we have that:} \\ \log _(1.01)50000\text{ = }t \\ \Rightarrow\text{ t = 1318.79 }\cong1319\text{ hours} \end{gathered}`

That is the number of hours it will take to get to 1000000 bacteria.