Question

1. write the letter (see bank of families below) of the corresponding function family associated with each representation.

i.

time in minutes	0	20	40	60	80	100	120

ii. the amount of the rivera’s monthly electric bill fluctuates (varies) throughout the year. it is highest in february and august and lowest in may and november.
iii. for a certain manufacturer the monthly sales of a product, s, in thousands of dollars, depends on the product’s selling price, p, and is modeled by the function s(p)= - 0.13(p - 14.8)^2+23.2
iv.

braking distance in feet	0	100	200	300	400

v. the function c(p)=\frac{3500}{p}+365 describes the average cost per person for a spring break trip for p people.
bank of function families:

a. linear	e. absolute value
c. even (square) root	g. rational
d. exponential	h. trigonometric

Explanation:

Step1: Analyze i

As time increases, the temperature of the water - bottle decreases in a non - linear way. This is an exponential decay situation, similar to Newton's Law of Cooling. So it is an exponential function.

Step2: Analyze ii

The monthly electric bill fluctuates throughout the year with a periodic pattern. This is a trigonometric function (sine or cosine) as it has a repeating pattern over time (a year).

Step3: Analyze iii

The function $S(p)=-0.13(p - 14.8)^{2}+23.2$ is in the vertex form of a quadratic function $y=a(x - h)^{2}+k$. So it is a quadratic function.

Step4: Analyze iv

The graph has a shape that starts with a rapid increase and then levels off, which is characteristic of an even (square) root function.

Step5: Analyze v

The function $C(p)=\frac{3500}{p}+365$ is a rational function since it is a quotient of two polynomials where the denominator is a non - zero polynomial.

Answer:

i. D. exponential
ii. H. trigonometric
iii. B. quadratic
iv. C. even (square) root
v. G. rational