Answer to Question #186908 in Algebra for allie frank

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 128 responses, but the responses were declining by 25% each day. Assuming the pattern continued, how many total responses would the company get over the course of the first 11 days after the magazine was published, to the nearest whole number

Answer 1

It follows that after second day the company got $128(1-0.25)=128\cdot 0.75=96$ responses. After third day the company got $128\cdot 0.75^2$ responses and so on. After 11th day the company got $128\cdot 0.75^{10}$ responses. Consequntly, total number of responses after 11 days is $128+128\cdot 0.75+...+128\cdot 0.75^{10}=128\frac{1-0.75^{11}}{1-0.75}\approx 490.$