Answer to Question #179968 in Algebra for Ava

Question

A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company got 50 responses, but the responses were declining by 10% each day. Assuming the pattern continued, how many total responses would the company get over the course of the first 12 days after the magazine was published, to the nearest whole number?

Answer 1

We have a geometric sequence

$a=50, r=100 \%-10\%=90\%=0.9\\ a_n=a\cdot r^{n-1}\\ a_n=50\cdot (0.9)^{n-1}\\ n=12\\ a_{12}=50\cdot (0.9)^{12-1}=50\cdot (0.9)^{11}=16$