Algebra 2 Exponential Growth and Decay Test Solutions and Scoring (PDF)

Algebra 2 math test solutions: Exponential Growth and Decay – Maths PDF

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This algebra 2 exponential functions test answers for Algebra 2 covers exponential growth and decay (Common Core F-LE.A.2, F-LE.B.5, A-SSE.B.3c, F-IF.C.8b), with a free PDF to print.

Use this answer key and scoring guide to grade the test on exponential growth and decay (F-LE.A.2). Each solution shows the full reasoning, and the scoring note explains how many points to award for correct setup, correct work, and a correct final answer. Partial credit rewards a sound method even when a small arithmetic slip changes the result.

Algebra 2 · Common Core State Standards: F-LE.A.2, F-LE.B.5, A-SSE.B.3c, F-IF.C.8b

Algebra 2 exponential functions test answers: worked solutions

Question 1 – Identify and evaluate [2 pts]

$b = 0.5 < 1$: decay. $f(3) = 6(0.125) = 0.75$.

Decay; f(3) = 0.75

Scoring: 1 point for the classification, 1 point for f(3).

Question 2 – Table to function [3 pts]

Initial value 4, ratio $12 \div 4 = 3$. So $f(x) = 4 \cdot 3^{x}$.

$f(5) = 4 \cdot 243 = 972$.

f(x) = 4·3^x; f(5) = 972

Scoring: 1 point for the initial value, 1 point for the growth factor, 1 point for f(5).

Question 3 – Percent growth [2 pts]

$P(t) = 8000(1.06)^{t}$. $P(3) = 8000(1.191016) \approx 9,528$.

About 9,528 people

Scoring: 1 point for the function, 1 point for the value.

Question 4 – Compound interest [3 pts]

$3000(1.06)^{4} \approx 3,787.43$
$3000(1.015)^{16} \approx 3,806.96$

(a) $3,787.43; (b) $3,806.96

Scoring: 1 point for each formula setup, 1 point for the correct values.

Question 5 – Half-life [2 pts]

15 years is 3 half-lives: $200\left(\frac{1}{2}\right)^{3} = 25$.

25 g

Scoring: 1 point for the number of half-lives, 1 point for the amount.

Question 6 – Graph features [2 pts]

Intercept (0, 3).

$f(0) = 3$. As $x$ increases, $f(x)$ approaches 0.

y-intercept (0, 3); asymptote y = 0; decreases toward 0

Scoring: 1 point for the intercept, 1 point for the asymptote and end behavior.

Question 7 – Equivalent rate [2 pts]

$1.005^{12t} = (1.005^{12})^{t}$. $1.005^{12} \approx 1.0617$.

About 6.2% per year

Scoring: 1 point for rewriting, 1 point for the rate.

Question 8 – Linear versus exponential [2 pts]

Plan values.

Week 4: $A = 220$, $B = 160$. Week 5: $A = 250$, $B = 320$.

Week 5

Scoring: 1 point for the comparison, 1 point for the week.

Question 9 – Find the error [2 pts]

$b = 0.9 = 1 – 0.10$, so the decay rate is 10% per step.

10% decay

Scoring: 1 point for the explanation, 1 point for the rate.

Total score

Total

20 points

Key facts behind this algebra 2 exponential functions test answers

Key facts

f(x) = a·b^x: a is the initial value, b the growth factor.
Growth factor b = 1 + r (growth) or 1 – r (decay).
Equal steps in x multiply the output by b.
Compound interest: A = P(1 + r/n)^(nt); continuous: A = Pe^(rt).
Rewrite b^x expressions to find equivalent rates.

How to use this algebra 2 exponential functions test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Algebra 2 chapters: Algebra 2 math.

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