Question

Bacteria quadruples on a daily basis. After the first day, there were 50 bacteria. Using the general exponential equation an=a1⋅r^n−1
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what value would represent a1

Answer 1

To find the value of \( a_1 \) in the exponential growth equation \( a_n = a_1 \cdot r^{n-1} \), we first need to identify the quantities involved:

- After the first day (which we can denote as day 1), the number of bacteria is 50.
- Since the bacteria quadruple each day, the growth factor \( r \) is 4.

In general, the equation for day \( n \) becomes:

\[
a_n = a_1 \cdot r^{n-1}
\]

For day 1 (where \( n = 1 \)), we have:

\[
a_1 = a_1 \cdot 4^{1-1} = a_1 \cdot 4^0 = a_1 \cdot 1 = a_1
\]

On this day, we know \( a_n = 50 \):

\[
50 = a_1 \cdot 1
\]

Therefore, we can conclude:

\[
a_1 = 50
\]

So, the value that would represent \( a_1 \) is **50**.