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

Answer:

C(19)=12 responses

Step-by-step explanation:

Exponential Decay Function

The exponential function is frequently used to model natural growing or decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function can be expressed as follows:

$C(t)=C_o\cdot(1-r)^t$

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

The company puts out an advertisement for a job opening. Initially, the company got 90 responses to the advertisement. Each day, the responses declined by 10%.

This is an example where the decay model can be used to calculate the responses to the advertisement at the day t.

The initial value is Co=90, the decaying rate is r=10% = 0.10. The model is written as:

$C(t)=90\cdot(1-0.1)^t$

Calculating:

$C(t)=90\cdot(0.9)^t$

We are required to calculate the number of responses at day t=19, thus:

$C(19)=90\cdot(0.9)^{19}$

C(19)=12 responses