# A single cholera bacteria divides every .05 hours to produce two complete cholera bacteria. If we...

## Question:

A single cholera bacteria divides every .05 hours to produce two complete cholera bacteria. If we start with a colony of 5,000 bacteria, then after t hours, there will be {eq}A(t) = 5000(2^{2t}) = 5000(4^t). {/eq}

Find A'(t).

Find A'(1).

Find A'(5) and interpret the results.

## Derivative:

We will first use the standard result to find the derivative of the function where we will plug-in the value of t to get the result.

To find the derivative of the function we will use:

{eq}A(t)=5000(4^{t}) {/eq}

Now using the standard result we will find the derivative:

{eq}A'(t)=5000(4^{t})\ln 4 {/eq}

a) Now let us plug-in the value of t:

{eq}A'(1)=5000(4)\ln 4\\ =27725.88 {/eq}

b) Now let us plug-in the value of t as 5:

{eq}A'(5)=5000(4^{5})\ln 4\\ =7097827.129 {/eq}