To determine the value of \( y \) for \( X = 19 \) days in the given equation \( y = 4.65 \cdot 1.37^x \):
1. Identify the given equation and values: The equation that models the stock is \( y = 4.65 \cdot 1.37^x \). Here, \( x \) represents the number of days, and we need to find \( y \) for \( x = 19 \).
2. Substitute \( x = 19 \) into the equation:
[tex]\[
y = 4.65 \cdot 1.37^{19}
\][/tex]
3. Calculate the exponentiation:
Calculate \( 1.37^{19} \). This step involves raising 1.37 to the 19th power.
4. Multiply by 4.65:
The resulting value from the exponentiation \( 1.37^{19} \) is then multiplied by 4.65.
Upon performing these calculations accurately, we find that the value of \( y \) is approximately \( 1841.38 \).
Therefore, the estimated value of stock \( XYZ \) at \( x = 19 \) days is:
[tex]\[
\boxed{\$1841.38}
\][/tex]
So, the correct answer is:
D. [tex]$\$[/tex]1841.38$
