Word of mouth advertising can be an effective form of marketing , or it can be very harmful. Consider a new restaurant that serves 27 customers on its opening night.
A) Of the 27 customers , 25 found the experience enjoyable and each told 3 friends over the next month. This group each told 3 friends over the next month , and so on, for six months. Assuming that no one heard twice, how many people have had a positive experience or heard positive reviews of the restaurant?
B) Suppose the 3 unhappy customers each told 6 friends over the next month about the experience. This group then each told 6 friends, and so on, for six months. Assuming that no one heard twice, how many people have had a negative experience or heard a negative review.
First question: Of the 27 customers, how can there be 25 happy and 3 unhappy?
in any case, just some the geometric progression, using the ratio r=3 or 6, as appropriate.
To answer these questions, we need to calculate the number of people who have had a positive or negative experience or heard positive or negative reviews of the restaurant over a period of six months.
A) For the first scenario, where 25 customers found the experience enjoyable and each told 3 friends over the next month, we can calculate the total number of people who have had a positive experience or heard positive reviews using exponential growth.
Here's how you can calculate it step by step for each month:
Month 1: 25 customers * 3 friends each = 75 positive experiences/reviews
Month 2: 75 friends * 3 friends each = 225 positive experiences/reviews
Month 3: 225 friends * 3 friends each = 675 positive experiences/reviews
Month 4: 675 friends * 3 friends each = 2025 positive experiences/reviews
Month 5: 2025 friends * 3 friends each = 6075 positive experiences/reviews
Month 6: 6075 friends * 3 friends each = 18,225 positive experiences/reviews
Therefore, over a period of six months, a total of 18,225 people have had a positive experience or heard positive reviews of the restaurant.
B) Now, let's calculate the number of people who have had a negative experience or heard a negative review for the second scenario, where 3 unhappy customers each told 6 friends over the next month.
Again, we'll calculate this step by step for each month:
Month 1: 3 customers * 6 friends each = 18 negative experiences/reviews
Month 2: 18 friends * 6 friends each = 108 negative experiences/reviews
Month 3: 108 friends * 6 friends each = 648 negative experiences/reviews
Month 4: 648 friends * 6 friends each = 3,888 negative experiences/reviews
Month 5: 3,888 friends * 6 friends each = 23,328 negative experiences/reviews
Month 6: 23,328 friends * 6 friends each = 139,968 negative experiences/reviews
So, over a period of six months, a total of 139,968 people have had a negative experience or heard a negative review of the restaurant.
Please note that these calculations assume no repeat information or double counting.
I hope this helps! Let me know if you have any further questions.