Writing exponential equations from context (SAT) is a grade 9 math skill aligned to Common Core standard HSF.LE.B.5. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 writing exponential equations from context (sat) problems our math games drill.
A warehouse begins a clearance week with boxes. Each week, half of the boxes still in the warehouse are shipped out. Which equation gives the number of boxes, , still in the warehouse after weeks?
The warehouse starts with boxes, and each week the remaining amount is multiplied by . After weeks, .
A town had residents in . Each year from through , a model estimates that the population increased by of the population the previous year. Which equation defines this model, where is the estimated population years after ?
The starting population is , and a yearly increase means multiplying by each year, so .
A phone is purchased for . Each year, a model estimates that the phone's value decreases by of its value the previous year. Which equation defines this model, where is the estimated value, in dollars, years after the purchase?
The starting value is , and a yearly decrease means multiplying by each year, so .
A forest preserve had acres of woodland in . Each year from through , a model estimates that the woodland area decreased by of the area the previous year. Which equation defines this model, where is the estimated woodland area, in acres, years after ?
The starting area is acres, and a yearly decrease means multiplying by each year, so .
A lab culture starts with cells. Each hour, a model estimates that the number of cells triples. Which equation defines this model, where is the estimated number of cells hours after the culture begins?
The starting count is , and tripling each hour means multiplying by , so .
An online course begins with students enrolled. Each week, a model estimates that of the students still enrolled withdraw. Which equation defines this model, where is the estimated number of students still enrolled weeks after the course begins?
The starting enrollment is , and a weekly withdrawal means remain, so multiply by each week: .
A charity drive starts with donors. Each day after the first day, a model estimates that the number of donors increases by of the number of donors the previous day. Which equation defines this model, where is the estimated number of donors days after the drive begins?
The starting number is , and a daily increase means multiplying by each day, so .
An art contest begins with entries. In each round, half of the entries still in the contest are cut. Which equation gives the number of entries, , still in the contest after round ?
The contest starts with entries, and each round multiplies the remaining count by . After round , .
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