# Express in exponential form : 5 bacteria triple every 15 minutes. How many after 3 hours?

How do I explain how to write this in exponential form in the easiest way possible such that a 5th grader can understand?

There were five bacteria in a dish at the beginning of an experiment. Every 15 minutes the bacteria in the dish tripled. Write in exponential form, the number of bacteria in the dish three hours after the experiment began.

Please note : It doesn't ask for the final answer,just to express it in exponential form.

• How many $15$-minute time-periods are there in $3$ hours? What do you do with this number? Where does the $5$ come in? Do yo know how to solve this problem? Start by trying to explain it to anyone at all, and then work on improving your explanation... – JavaMan Oct 15 '18 at 3:06
• Answering the JavaMan hints, notice there are 12 15-min time-periods. You multiply by 3. The 5 bacteria comes as +5. How would you model this then as an exponential form? – Bellatrix Oct 15 '18 at 3:09
• At the beginning, there are $5$ bacteria. After $15$ minutes, there are $5\cdot 3$ bacteria. After $30$ minutes, there are $5\cdot 3\cdot 3$ or $5\cdot 3^2$ bacteria. After $45$ minutes, there are $5\cdot 3\cdot 3\cdot 3$ or $5\cdot 3^3$ bacteria. The pattern keeps repeating. Keep in mind there are four $15$ minute periods in each hour, so can you take on from here? – KM101 Oct 15 '18 at 3:21
• Thank you everyone for your help. I found KM101's approach to be most effective in explaining ,since an organized list makes it easier to visually see the pattern.He is a 5th grader and just learned about exponents so this really helped! – Pearl Oct 15 '18 at 16:32
• Once he understood the pattern , I explained the hints and method that JavaMan and Isabella suggested. Thank you again everyone! – Pearl Oct 15 '18 at 16:41