Question

A restaurant has seen an increase in customers over the past three weeks, In the first week, 115 customers ate there. In the second week, the restaurant served 132 customers and in the third week, 149 customers ate at the restaurant. Make a conjecture about the number of customers who will eat there in the fourth week.

a. 122
b. 166
c. 176
d. 183

Answer 1

For this case we can model the problem by writing a linear equation of the form:
 $y = m (x-1) + b$
 Where,
 b: initial number of people
 m: rate of change
 x: number of weeks
 y: number of people
 We observe that the rate of change is constant and, therefore, the function is linear. The rate of change is 17 people per week.
 We have then:
 $m = 17$
 For week 1 the initial number of clients is:
 $b = 115$
 For the fourth week we have:
 $y = 17 * (4-1) +115 y = 166$
 Answer:
 the number of customers who will eat there in the fourth week is:
 b. 166

Answer 2

We have been given the number of customers that ate in three weeks.

Number of customers in 1st week = 115

Number of customers in 2nd week = 132

Number of customers in 3rd week = 149

If we collect all of them then we get sequence {115, 132, 149}

Notice that common difference between consecutive terms is constant which is 17

132-115=17

149-132=17

So that means, above sequence is arithmetic and hence we can use properties of sequence to find the next number in that sequence which can be easily obtained by adding 17 to the last number

149+17 = 166

Hence final answer is 166.