AP®︎ Precalculus: Topic 2.5 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 2.5 of AP Precalculus – Exponential Function Context and Data Modeling.

Questions List

Topic 2.5

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Question 1 Easy

Two savings plans each start with $1,000.

Plan A: $50 is added at the end of each month.

Plan B: The balance increases by 2% of the current balance at the end of each month.

Which statement correctly describes the balances as functions of the number of months?

ABoth Plan A's balance and Plan B's balance are exponential functions.
BBoth Plan A's balance and Plan B's balance are linear functions.
CPlan A's balance is a linear function, and Plan B's balance is an exponential function.
DPlan A's balance is an exponential function, and Plan B's balance is a linear function.

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Precalculus Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.

Topic 2.5: Exponential Function Context and Data Modeling

Learning Objective: 2.5.A

Construct a model for situations involving proportional output values over equal-length input-value intervals.

Essential Knowledge: 2.5.A.1

Exponential functions model growth patterns where successive output values over equal-length input-value intervals are proportional. When the input values are whole numbers, exponential functions model situations of repeated multiplication of a constant to an initial value.

Essential Knowledge: 2.5.A.2

A constant may need to be added to the dependent variable values of a data set to reveal a proportional growth pattern.

Essential Knowledge: 2.5.A.3

An exponential function model can be constructed from an appropriate ratio and initial value or from two input-output pairs. The initial value and the base can be found by solving a system of equations resulting from the two input-output pairs.

Essential Knowledge: 2.5.A.4

Exponential function models can be constructed by applying transformations to f(x)=abxf(x) = ab^x based on characteristics of a contextual scenario or data set.

Essential Knowledge: 2.5.A.5

Exponential function models can be constructed for a data set with technology using exponential regressions.

Essential Knowledge: 2.5.A.6

The natural base ee, which is approximately 2.718, is often used as the base in exponential functions that model contextual scenarios.

Learning Objective: 2.5.B

Apply exponential models to answer questions about a data set or contextual scenario.

Essential Knowledge: 2.5.B.1

For an exponential model in general form f(x)=abxf(x) = ab^x, the base of the exponent, bb, can be understood as a growth factor in successive unit changes in the input values and is related to a percent change in context.

Essential Knowledge: 2.5.B.2

Equivalent forms of an exponential function can reveal different properties of the function. For example, if dd represents number of days, then the base of f(d)=2df(d) = 2^d indicates that the quantity increases by a factor of 2 every day, but the equivalent form f(d)=(27)(d/7)f(d) = (2^7)^{(d/7)} indicates that the quantity increases by a factor of 272^7 every week.

Essential Knowledge: 2.5.B.3

Exponential models can be used to predict values for the dependent variable, depending on the contextual constraints on the domain, and may be used to determine values of the independent variable.

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