Question

real-world functions
for each real-world situation, determine whether it is modeled by a linear
function or a nonlinear function.

1. the graph models the number of

bacteria present on a surface over a
4-hour period.

1. the amount of a certain medication,

m, in the bloodstream after t hours can
be represented by the equation
b = -0.006t + 0.03.

1. the table shows the volume (v) of a

cube with various side lengths (s).

1. the graph models the path of a bottle

rocket from the time it is launched
until the time it reaches the ground
again.

1. a moving truck rental company

charges a flat rate of $45 for the day
plus an additional $0.65 per mile
driven. the amount a customer will
pay for a one-day rental is
represented by the equation
y = 0.65x + 45.

1. the table shows the perimeter (p) of a

square with various side lengths (s).

Explanation:

Problem 1:

Step1: Recall linear/nonlinear graph traits

Linear graphs are straight lines; nonlinear are curves.
The bacteria graph is a curve (exponential-like), not straight.

Step2: Classify the function

Since the graph is curved, it’s a nonlinear function.

Step1: Recall linear function form

Linear functions have the form \( y = mx + b \) (linear equation).
The equation \( b = -0.006t + 0.03 \) matches \( y = mx + b \) (m = -0.006, b = 0.03).

Step2: Classify the function

As it’s in linear equation form, it’s a linear function.

Step1: Recall volume of a cube formula

Volume of a cube: \( V = s^3 \) (nonlinear, cubic relationship).
Check table: \( s = 1 \to V = 1^3 = 1 \), \( s = 2 \to V = 2^3 = 8 \), etc. Matches \( V = s^3 \).

Step2: Classify the function

Since \( V = s^3 \) is nonlinear, the function is nonlinear.

Answer:

Nonlinear function

Problem 2: