few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Mathematical concept/skill options: 
A. Analyze proportional relationships and use them to solve real-world and mathematical problems.
B. Understand ratio concepts and use ratio reasoning to solve problems.


Your response:
B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000972

6
options: Define, evaluate, and compare functions.

Interpret functions that arise in applications in terms of the context.

Build a function that models a relationship between two quantities.

Construct and compare linear and exponential models and solve problems.

Interpret expressions for functions in terms of the situation they model.

Analyze functions using different representations.

Use functions to model relationships between quantities.

Prove and apply trigonometric identities.

Build new functions from existing functions.

Understand the concept of a function and use function notation.

Extend the domain of trigonometric functions using the unit circle.

Model periodic phenomena with trigonometric functions.
problem_activity: Task
In a carefully controlled biology lab, a population of 100 bacteria reproduces via binary fission. That is, every hour, on the hour, each bacteria splits into two bacteria. Assuming no bacteria deaths, find an expression for the number $P(t)$ of bacteria in the population after $t$ hours.
In the next lab over, a population of protists reproduces hourly according to multiple fission. The function which gives the population of protists after $t$ hours is $$P(t)=50\cdot 3^t.$$ Interpret the significance of the numbers 50 and 3 in the context of the biological experiment.


correct_option_index: 2

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