Answer :
We start with an initial helmet value of \[tex]$60,000. Every time a new movie is released, the helmet loses 8% of its value. Losing 8% means that the helmet retains 92% of its value from the previous movie release. In mathematical terms, after each movie, the value is multiplied by $[/tex]0.92[tex]$. This situation is represented by the exponential equation
$[/tex][tex]$
y = 60000 \cdot (0.92)^t,
$[/tex][tex]$
where $[/tex]t[tex]$ is the number of new movies released.
Thus, the correct equation from the multiple choice options is
$[/tex][tex]$
y=60000(0.92)^t.
$[/tex][tex]$
Next, we calculate the value of the helmet after 17 more movies. For $[/tex]t = 17[tex]$, the equation becomes
$[/tex][tex]$
y = 60000 \cdot (0.92)^{17}.
$[/tex][tex]$
Evaluating the expression $[/tex](0.92)^{17}[tex]$, we obtain approximately $[/tex]0.2423221228[tex]$. Multiplying this by \$[/tex]60,000 gives
[tex]$$
y \approx 60000 \cdot 0.2423221228 \approx 14539.3274.
$$[/tex]
Rounding to the nearest whole number, the helmet will be worth about \$14,539 after 17 movies.
$[/tex][tex]$
y = 60000 \cdot (0.92)^t,
$[/tex][tex]$
where $[/tex]t[tex]$ is the number of new movies released.
Thus, the correct equation from the multiple choice options is
$[/tex][tex]$
y=60000(0.92)^t.
$[/tex][tex]$
Next, we calculate the value of the helmet after 17 more movies. For $[/tex]t = 17[tex]$, the equation becomes
$[/tex][tex]$
y = 60000 \cdot (0.92)^{17}.
$[/tex][tex]$
Evaluating the expression $[/tex](0.92)^{17}[tex]$, we obtain approximately $[/tex]0.2423221228[tex]$. Multiplying this by \$[/tex]60,000 gives
[tex]$$
y \approx 60000 \cdot 0.2423221228 \approx 14539.3274.
$$[/tex]
Rounding to the nearest whole number, the helmet will be worth about \$14,539 after 17 movies.
