Sure, let's solve the problem step by step.
1. Identify the given information and the equation:
- We are given the equation [tex]\( y = 2x + 15 \)[/tex].
- [tex]\( x \)[/tex] represents the age of the coin in years.
- [tex]\( y \)[/tex] represents the value of the coin in dollars.
2. Substitute the given value of [tex]\( x \)[/tex] (the coin's age) into the equation:
- The age of the coin, [tex]\( x \)[/tex], is 19 years.
3. Perform the substitution:
- Substitute [tex]\( x = 19 \)[/tex] into the equation [tex]\( y = 2x + 15 \)[/tex].
- So, [tex]\( y = 2(19) + 15 \)[/tex].
4. Calculate the value step by step:
- First, calculate [tex]\( 2 \times 19 \)[/tex]:
[tex]\[ 2 \times 19 = 38 \][/tex]
- Then add 15 to this result:
[tex]\[ 38 + 15 = 53 \][/tex]
So, after 19 years, the value of the coin is \$53.
Therefore, the correct answer is:
[tex]\[ \boxed{53} \][/tex]
