Antonio made $18,000 in the first movie he ever starred in.He soon made more and more movies and more and more money.At a 46.18% rate of salary increase per movie,how many movies did he make in order to earn $5,350,000 in a single movie?
A)84 movies
B)34 movies
C)22 movies
D)15 movies

Question

Quizplus · Accepted Answer

Antonio's salary for each movie can be calculated using the formula for geometric progression: $S_n = S_1 \times (1 + r)^{n-1}$, where $S_n$ is the salary for the nth movie, $S_1$ is the initial salary, $r$ is the rate of increase, and $n$ is the number of movies. Given $S_1 = 18,000$, $r = 46.18\% = 0.4618$, and $S_n = 5,350,000$, we solve for $n$:$5,350,000 = 18,000 \times (1 + 0.4618)^{n-1}$.Solving for $n$ gives approximately 15, indicating Antonio made 15 movies to earn $5,350,000 in a single movie.

Antonio Made $18,000 in the First Movie He Ever Starred