2. Which situation can be modeled by a linear function?
A. The population of bacteria triples every day.
B. The value of a cell phone depreciates at a rate of 3.5% each year.
C. An amusement park allows 50 people to enter every 30 minutes.
D. A baseball tournament eliminates half of the teams after each round.
Din

Answer choice A and D have inconsistent values that'd be represented on a graph, thus not linear. Answer choice B is negative, leaving C as the only reasonable answer choice.

Answer Link

sqdancefan sqdancefan · Answer 2 · 2022-07-29T20:19:38+02:00

Answer:

C.

Step-by-step explanation:

A linear function is one that has a constant rate of change. The amount of change in any time interval is the same as for any other.

Evaluation of Choices

A. The amount of change from one day to the next is 2 times the number of bacterial on the previous day. That number varies daily, so cannot be represented by a linear function. The population is growing exponentially:

p = p₀(3^x)

B. The amount of depreciation this year is 3.5% of the value at the start of the year. That number changes yearly, so the value is not a linear function. The value is decreasing exponentially:

v = v₀(1 -0.035)^x

C. The number of people through the entrance is increasing by 50 each half hour. That number is constant, so the number entering can be represented by a linear function:

n = 100t . . . . where t is in hours

D. The number eliminated each round is half the number at the start of the round. This number changes with each round, so the number of teams is not a linear function. It can be represented by an exponential function:

t = t₀(1/2)^x