Bacteria quadruples on a daily basis. After the first day, there were 50 bacteria. Using the general exponential equation an = a1 · rn-1, what value would represent a1?

Answer 1

To determine the value of $a_1$ in the exponential equation $a_n=a_1\cdot r^{n-1}$, we need to analyze the given information:

1. The bacteria quadruples daily, which means $r=4$.
2. After the first day (which we will consider as $n=2$, since $n=1$ would represent the initial count), there are 50 bacteria.

The equation with the known values can be represented as:

$$a_2=a_1\cdot r^{2-1}$$ $$50=a_1\cdot 4^1$$ $$50=a_1\cdot 4$$

To find $a_1$, we can rearrange the equation:

$$a_1=\frac{50}{4}$$ $$a_1=12.5$$

Thus, the value that would represent $a_1$ is $12.5$.