few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Your response, in json format:
{
  "explanation": "An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation. Solving this problem does not require use of the Pythagorean identity.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001894

HS
options: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Distinguish between situations that can be modeled with linear functions and with exponential functions.

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
problem_activity: Task
Below is a table showing the approximate boiling point of water at different elevations:
{"table": [{"_attributes": {"class": ["regular"]}, "tbody": [{"tr": [{"th": [{"_value": "Elevation (meters above sea level)"}, {"_value": "Boiling Point (degrees Celsius)"}]}, {"td": [{"_value": "0"}, {"_value": "100"}]}, {"td": [{"_value": "500"}, {"_value": "98.2"}]}, {"td": [{"_value": "1000"}, {"_value": "96.5"}]}, {"td": [{"_value": "1500"}, {"_value": "94.7"}]}, {"td": [{"_value": "2000"}, {"_value": "93.1"}]}, {"td": [{"_value": "2500"}, {"_value": "91.3"}]}]}]}]}
Based on the table,
if we were to model the relationship between the elevation and the boiling point of water, would a linear function be appropriate? Explain why or why not.
Below are some additional values for the boiling point of water at higher elevations:
{"table": [{"_attributes": {"class": ["regular"]}, "tbody": [{"tr": [{"th": [{"_value": "Elevation (meters above sea level)"}, {"_value": "Boiling Point (degrees Celsius)"}]}, {"td": [{"_value": "5,000"}, {"_value": "83.2"}]}, {"td": [{"_value": "6,000"}, {"_value": "80.3"}]}, {"td": [{"_value": "7,000"}, {"_value": "77.2"}]}, {"td": [{"_value": "8,000"}, {"_value": "74.3"}]}, {"td": [{"_value": "9,000"}, {"_value": "71.5"}]}]}]}]}
Based on the table,
if we were to model the relationship between the elevation and the boiling point of water, would a linear function be appropriate? Explain why or why not.
When the information from both tables is combined, would a linear function be appropriate to model this data?  What kind of function would you use to model the data?  Why?


correct_option_index: 1

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