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 \( 12.5 \).