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 90
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 19 days after the magazine was
published, to the nearest whole number?

Answer 1

To calculate the total number of responses over the 19 days, a geometric series formula is used with the first term as 90 and the common ratio as 0.9, resulting in approximately 764 responses.

Step-by-step explanation:

The student asked how many total responses the company would get over the course of the first 19 days after the magazine with the job advertisement was published, assuming the pattern of declining responses by 10% each day continued.

To solve this problem, we use the formula for the sum of a geometric series, since each day the responses decline by a constant percentage, which makes the number of responses a geometrically decreasing sequence. The first term of the sequence (a1) is 90, the common ratio (r) is 0.9 (since the responses decline by 10%, or multiply by 0.9 each day), and the number of terms (n) is 19.

The sum of the first 19 terms of a geometric sequence is given by the formula:

Sn = a1 * (1 - rn) / (1 - r)

Plugging in the values we get:

S19 = 90 * (1 - 0.919) / (1 - 0.9)

S19 = 90 * (1 - 0.1512) / 0.1

S19 = 90 * 0.8488 / 0.1

S19 = 90 * 8.488

S19 ≈ 763.92

Rounded to the nearest whole number, the company would get approximately 764 responses over the course of the first 19 days.