MATH SOLVE

4 months ago

Q:
# 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. 122b. 166c. 176d. 183

Accepted Solution

A:

For this case we can model the problem by writing a linear equation of the form:

[tex]y = m (x-1) + b [/tex]

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:

[tex]m = 17 [/tex]

For week 1 the initial number of clients is:

[tex]b = 115 [/tex]

For the fourth week we have:

[tex]y = 17 * (4-1) +115 y = 166[/tex]

Answer:

the number of customers who will eat there in the fourth week is:

b. 166

[tex]y = m (x-1) + b [/tex]

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:

[tex]m = 17 [/tex]

For week 1 the initial number of clients is:

[tex]b = 115 [/tex]

For the fourth week we have:

[tex]y = 17 * (4-1) +115 y = 166[/tex]

Answer:

the number of customers who will eat there in the fourth week is:

b. 166