Question

which of the contexts below could be modeled by a linear function? answer an amusement park charges $4.00 to go on each of the rides. a towns population grows at a rate of 5.5% every year. a population of 500 bacteria doubles every week. a radioactive compound decays at a rate of 11% per hour.

Explanation:

Step1: Recall linear - function characteristics

A linear function has a constant rate of change.

Step2: Analyze each option

• For an amusement park charging $4.00 to go on each ride, if $y$ is the total cost and $x$ is the number of rides, then $y = 4x$. The rate of change (slope) is 4, a constant.
• For a town's population growing at a rate of 5.5% every year, the population $P$ after $t$ years is given by $P=P_0(1 + 0.055)^t$, which is an exponential - growth function.
• For a population of 500 bacteria that doubles every week, the population $P$ after $t$ weeks is $P = 500\times2^t$, which is an exponential - growth function.
• For a radioactive compound that decays at a rate of 11% per hour, the amount $A$ of the compound after $t$ hours is $A=A_0(1 - 0.11)^t=A_0\times0.89^t$, which is an exponential - decay function.

Answer:

An amusement park charges $4.00 to go on each of the rides.