DC CAPE Algebra I Linear, Quadratic, and Exponential Models Practice

Linear, Quadratic, and Exponential Models skills

construct and compare linear, quadratic, and exponential models and solve problems

interpret expressions for functions in terms of the situation they model

Standards basis

Common Core State Standards (CCSS-M) — District of Columbia

How the DC CAPE reports it

DC CAPE math continues DC’s PARCC-era alignment to the Common Core State Standards and uses the same general development/review approach described by OSSE. The page says DC Math follows the same rigorous development and review process and measures the knowledge and skills that matter most for DC students, while also explicitly tying the assessments to CCSS.

Blueprint & weighting

DC CAPE uses the PARCC-derived / Common Core-based framework (by grade domains structure).

Official sources

OSSE DC CAPE
OSSE DC CAPE page content on CCSS and test specifications

8 free questions · 0/0 correct

Practice playeasy

The function $S$ is defined by $S(t) = 450(0.85)^{t/3}$ . The function $S$ models the height, in centimeters, of a snowpack, where $t$ is the number of days after a winter storm. According to the model, what is the estimated height, in centimeters, of the snowpack $3$ days after the storm?

When $t = 3$ , the exponent is $3/3 = 1$ . So $S(3) = 450(0.85)^1 = 382.5$ centimeters.

Practice playeasy

A substance has a half-life of $1$ years. What fraction remains after $2$ years?

$2 \div 1 = 2$ half-lives. Remaining: $\left(\dfrac{1}{2}\right)^{2} = \dfrac{1}{4}$ .

Practice playeasy

Tree height, in feet, after $x$ years:
$\begin{array}{c|c} x & f(x) \\ \hline 1 & 20 \\ 2 & 28 \\ 3 & 36 \\ 4 & 44 \end{array}$
The height is $f(x)=mx+12\textsf{.}$ What is $m\textsf{?}$

Slope-intercept form is $f(x) = mx + b\textsf{.}$ The height increases by $8$ feet each year, so $m = 8\textsf{.}$

Practice playeasy

Plant height, in centimeters, after $x$ weeks:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline k(x) & 8 & 11 & 14 & 17 \end{array}$
Which of the following is $k(x)\textsf{?}$

The height increases by $3$ centimeters each week, and the starting height is $8$ centimeters. So $k(x) = 3x + 8\textsf{.}$

Practice playhard

A line has slope $\dfrac{2}{3}$ and passes through the point $(9, 10)$ . Which equation represents this line in standard form?

First write slope-intercept form: $10 = \dfrac{2}{3}(9) + b$ gives $b = 4$ , so $y = \dfrac{2}{3}x + 4$ . Multiplying by $3$ and rearranging gives $-2x + 3y = 12\textsf{.}$

Practice playmedium

Which value of $x$ satisfies $e^{x/2}=9$ ?

Take $\ln$ of both sides: $\dfrac{x}{2}=\ln 9$ . Multiply both sides by $2$ to get $x=2\ln 9\textsf{.}$

Practice playmedium

A town had $12{,}000$ residents in $2015$ . Each year from $2015$ through $2024$ , a model estimates that the population increased by $3\%$ of the population the previous year. Which equation defines this model, where $p(t)$ is the estimated population $t$ years after $2015$ ?

The starting population is $12{,}000$ , and a $3\%$ yearly increase means multiplying by $1.03$ each year, so $p(t) = 12{,}000(1.03)^t$ .

Practice playeasy

The function $g$ is defined by $g(n) = 80(1.12)^{n}$ . The function models the price, in dollars, of a limited-edition poster $n$ years after it was first sold. Which statement is the best interpretation of the growth factor $1.12$ in this context?

The growth factor is $1.12$ . Each time $n$ increases by $1$ , the price is multiplied by $1.12$ . That means each year the price is $112\%$ of the previous year's price, a $12\%$ increase.

DC CAPE Algebra I Linear, Quadratic, and Exponential Models. Practice it free.

Linear, Quadratic, and Exponential Models skills

construct and compare linear, quadratic, and exponential models and solve problems

interpret expressions for functions in terms of the situation they model

Topics mapped to this domain

Exponential functions in context (SAT)

Exponential and log formulas

Linear functions from tables (ACT/SAT)

Linear rule from a function table (ACT)

Slope-point line equations (ACT/SAT/PSAT 8/9/10)

Solving exponential equations with logarithms (ACT)

Writing exponential equations from context (SAT)

Interpreting exponential parameters

Interpreting linear parameters

Linear coefficient interpretations (SAT/PSAT 8/9/10)

8 free questions · 0/0 correct

Turn linear, quadratic, and exponential models into game time.

More Algebra I domains