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, in json format:
{
  "explanation": "This problem focuses on the ratio between two ingredients. Students do not have to analyze proportional relationships in-depth, which is reserved for a higher grade level, but rather use ratios to find missing values.",
  "answer": "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: Represent and solve problems involving addition and subtraction.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Understand solving equations as a process of reasoning and explain the reasoning.

Use properties of operations to generate equivalent expressions.

Add and subtract within 20.

Reason about and solve one-variable equations and inequalities.

Use the four operations with whole numbers to solve problems.

Understand and apply properties of operations and the relationship between addition and subtraction.

Understand properties of multiplication and the relationship between multiplication and division.

Rewrite rational expressions.

Solve equations and inequalities in one variable.

Solve systems of equations.

Generate and analyze patterns.

Represent and solve problems involving multiplication and division.

Work with equal groups of objects to gain foundations for multiplication.

Understand the connections between proportional relationships, lines, and linear equations.

Represent and analyze quantitative relationships between dependent and independent variables.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Perform arithmetic operations on polynomials.

Write and interpret numerical expressions.

Multiply and divide within 100.

Represent and solve equations and inequalities graphically.

Work with addition and subtraction equations.

Gain familiarity with factors and multiples.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Write expressions in equivalent forms to solve problems.

Interpret the structure of expressions.

Analyze patterns and relationships.

Work with radicals and integer exponents.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Use polynomial identities to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Create equations that describe numbers or relationships

Understand the relationship between zeros and factors of polynomials.
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: 26