Algebra 1 Exponential Functions and Growth Test Solutions and Scoring (PDF)

Algebra 1 math test solutions: Exponential Functions and Growth – Maths PDF

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This algebra 1 exponential functions test answers for Algebra 1 covers exponential functions and growth (Common Core F-LE.A.1, F-LE.A.2, F-LE.A.3, F-IF.C.7e, F-IF.C.8b), with a free PDF to print.

Use this key to grade the exponential functions test. Each solution shows the full work, and the scoring note explains how the points are awarded. The test totals 20 points. Give partial credit for correct steps, even when the final answer is wrong.

Algebra 1 · Common Core State Standards: F-LE.A.1, F-LE.A.2, F-LE.A.3, F-IF.C.7e, F-IF.C.8b

Algebra 1 exponential functions test answers: worked solutions

Question 1 – Growth or decay [2 pts]

a) $b = 1.3 > 1$: growth of 30%.

b) $b = 0.6 < 1$: decay of 40%.

a) growth, 30%; b) decay, 40%

Scoring: 1 point for each part.

Question 2 – Evaluate [2 pts]

$f(4) = 5 \cdot 16 = 80$.

$f(-1) = 5 \cdot 2^{-1} = 5 \cdot \frac{1}{2} = 2.5$.

80; 2.5

Scoring: 1 point for each value.

Question 3 – Write from a table [2 pts]

The starting value is 3 and the ratio is $\frac{6}{3} = 2$, $\frac{12}{6} = 2$.

$y = 3 \cdot 2^{x}$

Scoring: 1 point for the starting value; 1 point for the factor and equation.

Question 4 – Graph a decay function [2 pts]

Decay curve with y-intercept 3.

Values: $6, 3, 1.5, 0.75$. Plot them and draw a smooth decreasing curve.

Scoring: 1 point for correct values; 1 point for a correct curve.

Question 5 – Savings growth [2 pts]

a) $A = 500(1.08)^{t}$.

b) $500(1.08)^{3} = 500(1.259712) = 629.856 \approx 629.86$.

$A = 500(1.08)^{t}$; $629.86

Scoring: 1 point for the model; 1 point for the amount.

Question 6 – Solve [2 pts]

a) $125 = 5^{3}$, so $x = 3$.

b) $16 = 2^{4}$, so $x + 1 = 4$ and $x = 3$.

x = 3; x = 3

Scoring: 1 point for each part.

Question 7 – Car depreciation [3 pts]

a) $1 – 0.9 = 0.1$: 10% per year.

b) $30000(0.9)^{4} = 30000(0.6561) = 19683$.

c) After 3 years: $30000(0.9)^{3} = 21870$. After 4 years: 19,683, which is below 20,000.

10%; $19,683; year 4

Scoring: 1 point per part.

Question 8 – Linear versus exponential [3 pts]

Plan B passes Plan A between weeks 5 and 6.

a) Week 5: A has $350 and B has $320, so Plan A.

b) Week 6: A has $400 and B has $640, so Plan B.

c) Plan A adds a fixed $50 each week, but Plan B multiplies by 2, so the amount it adds keeps growing and soon exceeds $50.

Plan A; Plan B; B multiplies

Scoring: 1 point per part.

Question 9 – Half-life [2 pts]

$A = 120\left(\frac{1}{2}\right)^{t/4}$.

For $t = 12$: $120\left(\frac{1}{2}\right)^{3} = 120 \cdot \frac{1}{8} = 15$.

15 mg

Scoring: 1 point for the model; 1 point for the amount.

Total score

Total

20 points

Key facts behind this algebra 1 exponential functions test answers

Key facts

Exponential form: f(x) = a·bˣ with a the starting value and b the factor.
Growth: b = 1 + r. Decay: b = 1 – r.
Linear functions add a constant; exponential functions multiply by a constant.
Compound interest: A = P(1 + r)ᵗ.
An exponential function eventually exceeds any linear function.

How to use this algebra 1 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 1 chapters: Algebra 1 math.

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