The equation [tex]$y = 4.65 \cdot 1.37^x[tex]$[/tex] fits the graph of stock [tex]$[/tex]XYZ[tex]$[/tex] over the past month with an [tex]$[/tex]r[tex]$[/tex]-value of 0.9894. How much do you think [tex]$[/tex]XYZ[tex]$[/tex] will be worth at [tex]$[/tex]x = 19$[/tex] days?

A. [tex]$\[tex]$ 137.44$[/tex][/tex]
B. [tex]$\[tex]$ 465.12$[/tex][/tex]
C. [tex]$\[tex]$ 989.49$[/tex][/tex]
D. [tex]$\[tex]$ 1841.38$[/tex][/tex]



Answer :

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]$\$[/tex]1841.38$