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
.
Remaining Attempts : 3

Answer 1

its wrong

Answer 2

In the provided exponential equation \( a_n = a_1 \cdot r^{n - 1} \), \( a_n \) represents the amount of bacteria after \( n \) days, \( a_1 \) is the initial amount of bacteria, and \( r \) is the growth factor.

Given that the bacteria quadruples daily, the growth factor \( r = 4 \). According to the problem, after the first day (when \( n = 1 \)), there are 50 bacteria, which means \( a_2 = 50 \).

So, applying the equation for \( n = 2 \):

\[
a_2 = a_1 \cdot r^{n - 1}
\]

We can substitute the values:

\[
50 = a_1 \cdot 4^{2 - 1}
\]

This simplifies to:

\[
50 = a_1 \cdot 4
\]

To find \( a_1 \), divide both sides by 4:

\[
a_1 = \frac{50}{4} = 12.5
\]

Thus, the value of \( a_1 \) is **12.5**.