Question

Daniel wrote the function F(x) = 5(1.2) to model a situation given on her homework. Which of the following problem situations can be described using this function rule?

A) A bacteria sample started with 5 bacteria increases at a rate of 20% every hour. Write a function that can be used to describe the amount of bacteria in the sample after any number of hours.
B) A school bus starts its morning route with 5 passengers at its first stop. At each bus stop along the route, 2 people on average get onto the bus. Write a function that can be used to describe the number of people on the bus at any given stop along the route to school.
C) Marcus opens a savings account with an initial deposit of $5.00. Each week Marcus deposits $1.20 into his account. Write a function rule that can be used to find the amount of money Marcus has deposited in his account after any number of weeks.
D) A coffee maker reservoir holds 5 gallons of water. After each cup of coffee brewed, the water level is reduced by 20%. Write a function rule that can be used to describe the portion of the original 5 gallons of water that is remaining in the reservoir after a given number of cups brewed.

Answer 1

The function F(x) = 5(1.2)^x accurately represents a situation where a bacteria sample starting with 5 bacteria increases at a rate of 20% every hour, exemplifying exponential growth. The option A from the provided situations fits this model.

Step-by-step explanation:

Daniel wrote the function F(x) = 5(1.2)^x to model a situation given on her homework. The correct problem situation that can be best described using this function rule is: A) A bacteria sample started with 5 bacteria increases at a rate of 20% every hour.

This is an example of an exponential growth model, where the quantity increases by a consistent percentage over equal increments of time. In this situation, we are starting with 5 bacteria, and each hour, the population increases by 20%, which is represented by multiplying by 1.2 (100% + 20% = 120% = 1.2) for each hour x.

The other options do not fit this exponential model, as they either involve linear increases, additions, or reductions by a constant amount rather than a percentage.