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Digital SAT Math : Nonlinear functions -Practice Questions

Digital SAT Math : Nonlinear functions -Practice Questions - New Syllabus

DSAT MAth Practice questions – all topics

  • Advanced Math Weightage: 35% Questions: 13-15
    • Equivalent expressions
    • Nonlinear equations in one variable and systems of equations in two variables
    • Nonlinear functions

DSAT MAth and English  – full syllabus practice tests

Question Easy

The function \( f(x) = 200,000 \cdot (1.21)^x \) gives a company’s predicted annual revenue, in dollars, \( x \) years after the company started selling light bulbs online, where \( 0 < x \leq 10 \). What is the best interpretation of the statement “f(5) is approximately equal to 518,748” in this context?

A. 5 years after the company started selling light bulbs online, its predicted annual revenue is approximately 518,748 dollars.

B. 5 years after the company started selling light bulbs online, its predicted annual revenue will have increased by a total of approximately 518,748 dollars.

C. When the company’s predicted annual revenue is approximately 518,748 dollars, it is 5 times the predicted annual revenue for the previous year.

D. When the company’s predicted annual revenue is approximately 518,748 dollars, it is 5% greater than the predicted annual revenue for the previous year.

▶️ Answer/Explanation
Solution

Ans: A

The function \( f(x) = 200,000 \cdot (1.21)^x \) gives the predicted annual revenue \( x \) years after starting online sales.

\( f(5) \approx 518,748 \) means the revenue at \( x = 5 \) is approximately 518,748 dollars.

Thus, it represents the predicted annual revenue 5 years after starting.

Choice B: Incorrect, it measures total increase, not revenue.

Choice C: Incorrect, 5 times is not implied.

Choice D: Incorrect, 5% increase is not supported.

Question Easy

Graph of Plant Diversity vs Elevation

The quadratic function graphed above models a particular measure of plant diversity as a function of the elevation in a region of Switzerland. According to the model, which of the following is closest to the elevation, in meters, at which plant diversity is greatest?

A. 13,500

B. 3,000

C. 1,250

D. 250

▶️ Answer/Explanation
Solution

Ans: C

The graph shows plant diversity (\( y \)) versus elevation (\( x \)).

The greatest plant diversity is the peak of the parabola, at approximately \( y = 13,500 \).

The corresponding elevation (\( x \)) is around 1,250 meters.

Choice A: Incorrect, 13,500 is the diversity, not elevation.

Choice B: Incorrect, at 3,000 meters, diversity is near 0.

Choice D: Incorrect, at 250 meters, diversity is around 11,000, not the maximum.

Question Easy

Graph of City Population Model

The graph shown models the number of residents of a certain city \( x \) years after 2010. How many residents does this model estimate the city had in 2010?

A. 0

B. 2,000

C. 20,000

D. 25,000

▶️ Answer/Explanation
Solution

Ans: C

Since \( x \) is years after 2010, \( x = 0 \) represents 2010.

The graph shows the y-value at \( x = 0 \) is 20,000.

Thus, the model estimates 20,000 residents in 2010.

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