Advanced Math · Exponential And Radical Equations
SAT Exponential And Radical Equations Practice Questions (Free + Explanations) | Quiz 1
A bacteria culture starts with bacteria and doubles every hour. According to this model, how many bacteria will there be after hours?
When a quantity doubles every hour, it is multiplied by each hour. After hours, the number of bacteria is . So the correct answer is .
Exponential growth means multiplying by the same factor over equal time intervals. For doubling, use the form .
If , what is the value of ?
Since , the equation can be written as . Therefore, .
To solve a basic exponential equation, rewrite both sides with the same base and then set the exponents equal.
Which expression is equivalent to ?
To rewrite , factor as a perfect square times another factor: . Then
So the equivalent expression is .
To simplify a radical, factor the number inside the square root into a perfect square and another factor, then take the square root of the perfect square.
The graph of is shown in the -plane. Which coordinate lies on the graph?
To find a point on the graph of , substitute the -value into the expression. If , then . So lies on the graph.
A point lies on a graph if its coordinates satisfy the equation. For a radical function, substitute the given -value and evaluate the square root.
A point lies on the graphs of both equations below.
What is the value of ?
Because the point lies on both graphs, the two expressions for must be equal. So . Squaring both sides gives , so .
In a system, both equations must be true at the same point. If one equation gives a value of , substitute that value into the other equation and solve.
Your results
Estimated SAT Math band
500-550
Illustrative range from this short quiz—not an official College Board score.
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More SAT Math practiceYour results
Estimated SAT Math band
500-550
Illustrative range from this short quiz—not an official College Board score.
Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.
More SAT Math practiceYour results
Estimated SAT Math band
600-650
Illustrative range from this short quiz—not an official College Board score.
Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.
More SAT Math practiceYour results
Estimated SAT Math band
600-650
Illustrative range from this short quiz—not an official College Board score.
Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.
More SAT Math practiceYour results
Estimated SAT Math band
700+
Illustrative range from this short quiz—not an official College Board score.
Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.
More SAT Math practiceYour results
Estimated SAT Math band
700+
Illustrative range from this short quiz—not an official College Board score.
Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.
More SAT Math practice