SAT Two-variable data: models and scatterplots Practice Question 14 (Medium)

Question bank / Two-variable data: models and scatterplots

Math · Problem-Solving and Data AnalysisMedium

Time (hours)	0	2	4
Number of bacteria	200	800	3,200

The table shows the number of bacteria in a culture at selected times. Which of the following equations best models the number of bacteria $y$ after $t$ hours?

$y = 200(4)^t$

$y = 300t + 200$

$y = 200(1.5)^t$

$y = 200(2)^t$

Show answer and explanation

Answer: D

The count is multiplied by $4$ every $2$ hours ( $800 \div 200 = 4$ and $3200 \div 800 = 4$ ), so the growth is exponential. Multiplying by $4$ every $2$ hours means multiplying by $2$ every hour. With an initial count of $200$ , the model is $y = 200(2)^t$ . Check: at $t = 4$ , $200(16) = 3{,}200$ .

Choice A uses $4$ as the hourly growth factor, but the count quadruples every $2$ hours, not every hour.

Ask Owl about this question Next question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free.