<p>A piece of raw meat is accidentally left out at room temperature, and bacteria begin to grow on it. Initially, there are \(500\) bacteria presents, and the number of bacteria doubles every \(3\) hours. The number of bacteria, \(N\), after \(t\) hours can be modelled by the formula \(N = 500(2)^{kt}.\)</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">Show that&nbsp;\(k = \frac{1}{3}\).<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">It is considered unsafe for consumption when the number of bacteria on the meat exceeds \(3\ 000\). Determine the maximum number of hours that it will still be safe to consume the meat.<span class="inline-marks">[3]</span></div></li></ol>

A piece of raw meat is accidentally left out at room temperature, and bacteria begin to grow on it. Initially, there are \(500\) bacteria presents, and the number of bacteria doubles every \(3\) hours. The number of bacteria, \(N\), after \(t\) hours can be modelled by the formula \(N = 500(2)^{kt}.\)

It is considered unsafe for consumption when the number of bacteria on the meat exceeds \(3\ 000\). Determine the maximum number of hours that it will still be safe to consume the meat.

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions