standard_description: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
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.
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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?


aligns: no