Question

1. A daycare center charges a $100 sign up fee, plus $50 per week. Write an equation that represents the total cost, f(x), for x weeks.

f(x) = _____x + ______


a. Identify the rate of change and interpret its meaning in the context of the problem.



b. Identify the y-intercept and interpret its meaning in the context of the problem.



c. What does x represent? What does f(x) represent?



d. Find the cost for a baby to attend daycare for 12 weeks. Write your answer using function notation.



e. Calculate f(-3). Explain what this question is asking you to find in the context of the problem, then discuss the reasonanbleness of this question and its answer.

Answer 1

f(x)=50x+100

a)rate of change is 50

b)y-intercept is 100

c)x represents the no. of weeks

f(x) represents the the total cost for x weeks.

d)f(12)=700

e)Cost and week cannot be negative

Explanation:

Sign up fee at daycare = $100

Cost of 1 week = 50

Cost of x weeks = 50 x

So, Total cost = 100+50x

Thus f(x)=50x+100

a)

General equation : y=mx+c

m = slope = rate of change

On comparison

m = 50

So, rate of change is 50

50 is the cost of daycare per week

b)

y intercept : y intercept is a point where a line 's graph intersects (crosses) the Y-axis i.e. x=0

Substitute x = 0 in equation

f(x)=50(0)+100

f(0)=100

So, y-intercept is 100

$100 is a signup fee

c)

x represents the no. of weeks

f(x) represents the the total cost for x weeks.

d)

Substitute x = 12

So, Cost for a baby to attend daycare for 12 weeks:

f(12)=50(12)+100

f(12)=700

e)

f(-3)=50(-3)+100=-50

Here it is asking about negative 3 weeks which is not possible

Since no. of weeks cannot be negative

On solving we are getting the negative total cost

Cost and week cannot be negative