This algebra 1 exponential test answer key gives the full solution and the scoring guide for each of the 8 test questions on exponential growth and decay.
Worked solutions and scoring guides for all eight questions, 20 points in total. Award each point separately. Accept any correct equivalent form, such as 1.25 for a quarterly rate written as a decimal, as long as the work is clear.
Algebra 1 Exponential Test Answer Key: questions 1–5
Question 1: Table to equation (2 points)
- \(6: 3=2\), \(12: 6=2\): the factor is 2.
- \(a=3\) (the value at \(x=0\)) and \(b=2\): \(y=3(2)^{x}\).
Scoring: 1 point for the factor 2, 1 point for the equation with a = 3.
Question 2: Classify tables (2 points)
- The differences are all 5: linear.
- The ratios are all \(12: 4=3\): exponential with factor 3.
Scoring: 1 point for each correct classification with a valid reason.
Question 3: Growth and decay rates (2 points)
- Start 1500, 6% growth per year.
- Start 60, 25% decay per year (\(1-0.75=0.25\)).
Scoring: 1 point for each part, both the starting value and the percent with growth or decay.
Question 4: Write and use exponential models (3 points)
- \(P(t)=8000(1.025)^{t}\)
- \(8000(1.025)^{10}=8000\times 1.2801\approx\)\(10,241\) people.
- \(V(t)=18000(0.88)^{t}\)
Scoring: 1 point for each part. In (a) and (c), 0 points if the factor is 2.5 or 12 or 0.12.
Question 5: Reading an exponential graph (3 points)
- \(a=4\) (the \(y\)-intercept) and \(b=2: 4=\frac{1}{2}\).
- \(y=4(\frac{1}{2})^{x}\). Check: \(4(\frac{1}{2})^{2}=1\).
- \(y\) decreases and gets closer and closer to 0 but never reaches it.
Scoring: 1 point for a and b, 1 point for the equation, 1 point for describing decay toward 0 without reaching it.
Algebra 1 Exponential Test Answer Key: questions 6–8
Question 6: Compound interest (3 points)
- \(P=3000\), \(r=0.04\), \(n=4\), \(t=2\): \(A=3000(1+\frac{0.04}{4})^{8}=3000(1.01)^{8}\).
- \(1.01^{8}\approx1.082857\), so \(A\approx\)\(\$3,248.57\).
- \(3248.57-3000=\)\(\$248.57\).
Scoring: 1 point for correct substitution (n = 4, exponent 8), 1 point for the balance, 1 point for the interest.
Question 7: Exponential versus linear (3 points)
- Curve A: it curves upward and multiplies by 3 for each step in \(x\); Curve B is a straight line that adds 10 each step.
- \(x=3\): \(32>27\). \(x=4\): \(81>42\). The first whole number is \(x=4\).
- Each step adds 10 to the line, but each step multiplies Curve A by 3, adding at least \(2\cdot3^{4}=162\) at the next step. The gap only widens.
Scoring: 1 point for Curve A with a reason, 1 point for x = 4 with both values shown, 1 point for an explanation that compares constant addition with multiplication.
Question 8: Interpret a model (2 points)
- 1200 is the number of subscribers at launch (\(t=0\)). 1.15 means the count grows to 115% each month, a 15% increase per month.
- \(1200(1.15)^{3}=1200\times 1.520875=\)\(1,825\) subscribers.
Scoring: 1 point for both meanings, 1 point for 1,825.
Scoring summary
20 points: add the points of every question of this algebra 1 exponential test answer key.
How to use this algebra 1 exponential test answer key
Use this algebra 1 exponential test answer key to score the test fairly and to see which skills need more practice.
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Algebra 1 Exponential Growth and Decay test answer key
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