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 70 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 23 days after the magazine was published, to the nearest whole number?

Answer 1

638

Explanation:

The total number of responses is the value of a geometric series with first term 70 and common ratio 1-10% = 0.90. That sum is given by the formula ...

Sn = a1·(1 -r^n)/(1 -r)

where r is the common ratio, n is the number of terms, and a1 is the first term.

The sum of n=23 terms of the series with a1=70 and r=0.9 is ...

S23 = 70·(1 -0.9^23)/(1 -0.9) = 700(1 -0.9^23) ≈ 638

The model predicts 638 total responses over the first 23 days.