Question

A company is trying out a new marketing technique that begin by asking One customer to tell three friends about a product in the first week the next week each of those new customers tells three friends so three new people know about the product the first week 9 the second week in 27 the third week let W represent the number of weeks which algebraic expression models the situation

a. 3w
b. w^3
c. 3^w
d. 3w^3

Answer 1

Week 1 : 1 customer tells 3 friends

Week 2: 3 new customers tell 9 friends

Week 3: 9 new customers tell 27 friends

If w represents number of weeks, then (C) represents the model appropriately. Let's see how:

Putting w = 1 , 2 and 3 in each of the options

(A) 3w: 3 for week 1, 6 for week 2, 9 for week 3 ⇒ INCORRECT

(B) w^3: 1 for week 1, 8 for week 2, 27 for week 3 ⇒ INCORRECT

(C) 3^w: 3 for week 1, 9 for week 2, 27 for week 3 ⇒ CORRECT

(D) 3w^3: 3 for week 1, 24 for week 2, 81 for week 3 ⇒ INCORRECT

Hence, the answer is (C)

Answer 2

Answer: Option 'c' is correct.

Explanation:

Since we have given that

Number of product in first week = 3

Number of product in second week = 9

Number of product in third week = 27

Let the number of week be 'w'.

So, algebraic expression of the number of product in w weeks would be

`3^w`

Hence, Option 'c' is correct.