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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Rewrite rational expressions.

Add and subtract within 20.

Create equations that describe numbers or relationships

Represent and solve problems involving multiplication and division.

Use the four operations with whole numbers to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Understand the relationship between zeros and factors of polynomials.

Work with addition and subtraction equations.

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

Use properties of operations to generate equivalent expressions.

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

Perform arithmetic operations on polynomials.

Write and interpret numerical expressions.

Solve equations and inequalities in one variable.

Solve systems of equations.

Generate and analyze patterns.

Represent and solve problems involving addition and subtraction.

Use polynomial identities to solve problems.

Write expressions in equivalent forms to solve problems.

Multiply and divide within 100.

Interpret the structure of expressions.

Work with radicals and integer exponents.

Analyze patterns and relationships.

Reason about and solve one-variable equations and inequalities.

Represent and solve equations and inequalities graphically.

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

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

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

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

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

Gain familiarity with factors and multiples.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.
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: 22