I'm in 9th grade, and I'm having some difficulties completing a math assignment in my Algebra 1 class. My question is about exponential growth.
If I start off with 1 bacteria, and it triples every hour, how many will I have after 24 hours? If you answer this, please walk me through the steps. It would be greatly appreciated!
One more question. What would the formula for this situation be? ($y=a(1+r)^x$)
Best Answer
Consider what is actually happening in the question.
You begin with 1 bacteria, and after 1 hour it has tripled so you now have $1$ x $3=3$.
Next hour, it triples again so you now have $1$ x $3$ x $3=9$
You can see the pattern shows that the number of bacteria is multiplying every hour by a factor of 3. An exponent denotes how many times we are multiplying a number by itself, for example: $3^4$ means we are multiplying the number 3 a total of 4 times ($3$ x $3$ x $3$ x $3$).
Therefore the question is requiring us to triple the number of bacteria every hour for 24 hours, which means we are multiplying by 3 a total of 24 times. This gives us:
$n$ x $3^{24}$ where n is the number of bacteria you begin with.
Since you begin with 1 bacteria, the solution is $1$ x $3^{24}=3^{24}$