few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


Standard options: 
A. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.


Your response, in json format:
{
  "explanation": "This task asks students to compare two fractions that are equal. The two fractions have different numerators and denominators (e.g. 1/4 and 3/12). The students need to explain why the two fractions are equal by drawing a picture, which involves using visual fraction models.",
  "answer": "A, B"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_000212

4
options: 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.

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

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

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).
problem_activity: Problem 1
Malik bought a new car for $15,000. As he drove it off the lot, his best friend, Will, told him that the car’s value just dropped by 15% and that it would continue to depreciate 15% of its current value each year.
If the car’s value is now $12,750 (according to Will), what will its value be after 5 years? Complete the table below to determine the car’s value after each of the next five years. Round each value to the nearest cent.
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "table-layout:fixed; width:80%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "strong": [{"em": [{"_value": "t"}], "_values": ["# of years,", ", since driving the car off the lot"]}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"em": [{"_value": "t"}], "_values": ["Car value after", "years"]}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "15% depreciation of current value"}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Car value minus 15% depreciation"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "0"}, {"_attributes": {"style": "text-align:center"}, "_value": "$12,750.00"}, {"_attributes": {"style": "text-align:center"}, "_value": "$1,912.50"}, {"_attributes": {"style": "text-align:center"}, "_value": "$10,837.50"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "1"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "2"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "3"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "5"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {}]}]}]}]}
Write an exponential function to model the value of Malik’s car
$$t$$
years after driving it off the lot.
Use the function from part (b) to determine the value of Malik’s car 5 years after its purchase. Round your answer to the nearest cent. Compare the value with the value in the table. Are they the same?
Use the function from part (b) to determine the value of Malik’s car 7 years after its purchase. Round your answer to the nearest cent.
Problem 2
Every day Brian takes 20 mg of a drug that helps with his allergies. His doctor tells him that each hour the amount of drug in his bloodstream decreases by 20%.
Construct an exponential function in the form
$${f(t)=ab^t}$$
, for constants
$$a$$
and
$$b$$
, that gives the quantity of the drug, in milligrams, that remains in Brian’s bloodstream
$$t$$
hours after he takes the medication.
How much of the drug remains one day after taking it?
Do you expect the percentage of the dose that leaves the bloodstream in the first half hour to be more than or less than 20%? What percentage is it?
How much of the drug remains one minute after taking it?


correct_option_index: 1