Question

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 ?(1 point) The value of a1 is .

Answer 1

The general exponential equation is given by:

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

where:
- \( a_n \) is the amount of bacteria after \( n \) days,
- \( a_1 \) is the initial amount of bacteria,
- \( r \) is the growth factor (in this case, the bacteria quadruples each day, so \( r = 4 \)),
- \( n \) is the number of days.

From the information given:
- After the first day (\( n = 1 \)), the amount of bacteria is 50.

Since we want to find \( a_1 \) (the initial amount), we can set up the equation for the first day:

\[
a_1 \cdot r^{1-1} = 50
\]

This simplifies to:

\[
a_1 \cdot 4^{0} = 50
\]
\[
a_1 \cdot 1 = 50
\]
\[
a_1 = 50
\]

Thus, the value of \( a_1 \) is \( 50 \).