Linear Exponential Patterns Quiz: Distinguishing Linear and Exponential Patterns

  • 9th Grade
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| Attempts: 12 | Questions: 20 | Updated: Dec 17, 2025
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Question 1 / 21
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1) Identify the pattern: 5, 9, 13, 17, ...

Explanation

Consecutive differences are 4, 4, 4 which are constant. Constant difference implies a linear pattern.

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About This Quiz
Linear Exponential Patterns Quiz: Distinguishing Linear and Exponential Patterns - Quiz

How can you tell whether a pattern is growing linearly or exponentially? In this quiz, you’ll examine tables, graphs, and descriptions to spot whether values change by a constant amount or a constant factor. You’ll compare sequences, analyze the shape of growth, and connect each pattern to real-life situations like... see moresavings, temperature, or population data. Step by step, you’ll develop a clear sense of how linear and exponential trends behave and why they differ so sharply.
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2) Identify the pattern: 3, 6, 12, 24, ...

Explanation

Consecutive ratios are 6/3 = 2, 12/6 = 2, 24/12 = 2 which are constant. Constant ratio implies an exponential pattern.

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3) If a quantity increases by the same amount every equal time interval, the model is linear.

Explanation

Linear change has constant difference Δy per step. Equal additive change defines linear growth or decay.

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4) For the sequence 2, 6, 18, 54, ... the common ratio is:

Explanation

Ratios: 6/2 = 3, 18/6 = 3, 54/18 = 3. Constant ratio 3 implies exponential growth with base 3.

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5) Select all linear functions.

Explanation

Linear functions have the form y = mx + b (constant slope). A: slope 4. C: constant function is linear with slope 0. E: slope −5. B is exponential; D is quadratic.

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6) For y(n) = 5·3^n, the value at n = 0 equals ____.

Explanation

At n = 0 we have 3^0 = 1, so y(0) = 5·1 = 5.

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7) Select all sequences that are exponential (with nontrivial base b ≠ 1).

Explanation

A: ratios 27/81 = 1/3, 9/27 = 1/3, 3/9 = 1/3 ⇒ exponential with base 1/3. E: ratios are 3. B has constant difference (linear). C has neither constant difference nor constant ratio. D has base 1 (trivial), excluded by b ≠ 1 in this question.

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8) If successive ratios y_{n+1}/y_n are equal for all n (and y_n ≠ 0), the pattern is exponential.

Explanation

A constant ratio r means y_n = y_0·r^n, which is exactly the definition of an exponential sequence.

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9) Which function models “starting at 50 and growing by 8% per day”?

Explanation

A constant 8% per day means multiply by 1.08 each day: y = 50·(1.08)^t. Option A adds a constant amount instead of a constant percent. Option D is 8% decay.

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10) A linear model can represent decrease using a negative slope.

Explanation

For y = mt + b, a negative slope m

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11) A quantity has values 100, 90, 80, 70 at t = 0,1,2,3. Which model fits?

Explanation

Differences are −10 each step (constant difference). That is linear decay with slope −10 per unit time.

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12) A quantity has values 200, 160, 128, 102.4 at t = 0,1,2,3. Which model fits?

Explanation

Ratios are 160/200 = 0.8, 128/160 = 0.8, 102.4/128 = 0.8 (constant). Constant ratio

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13) The function y = 500(1.02)^t adds 2 units each time step.

Explanation

y = a·b^t multiplies by a constant factor b each step. Here b = 1.02 means a 2% multiplicative increase, not adding 2 units.

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14) Which function has a constant percent rate of change?

Explanation

Exponential models y = a·b^t have constant percent change (b − 1)·100%. Linear y = mt + b changes by a constant amount, not a constant percent.

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15) Identify the model: y = 7 − 0.4x.

Explanation

The equation is of the form y = mx + b with slope m = −0.4 and intercept 7, so it is linear (a constant additive change −0.4 per unit x).

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16) Select all true statements about linear vs exponential change.

Explanation

A: definition of linear. B: definition of exponential. C: base between 0 and 1 gives decay. D is false because linear has constant additive change, so percent change varies with level. E is true since percent change equals (b − 1)·100%.

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17) Consider values 5, 8, 12, 18 at t = 0,1,2,3. Which model fits best?

Explanation

Differences are 3, 4, 6 (not constant). Ratios are 8/5 = 1.6, 12/8 = 1.5, 18/12 = 1.5 (not constant). With neither constant difference nor constant ratio, neither linear nor exponential fits exactly.

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18) For y = 2.5x + 7, the amount added each time x increases by 1 is ____.

Explanation

In y = mx + b, the coefficient m is the slope, which is the constant difference per unit increase in x. Here m = 2.5.

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19) For the sequence 7, 10, 13, 16, ... the common difference is ____.

Explanation

Differences: 10−7 = 3, 13−10 = 3, 16−13 = 3. Constant difference 3 confirms linearity.

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20) Find the common ratio for 240, 180, 135, 101.25, ...

Explanation

Compute consecutive ratios: 180/240 = 0.75, 135/180 = 0.75, 101.25/135 = 0.75. Constant ratio 0.75 indicates exponential decay by 25% each step.

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Identify the pattern: 5, 9, 13, 17, ...
Identify the pattern: 3, 6, 12, 24, ...
If a quantity increases by the same amount every equal time interval,...
For the sequence 2, 6, 18, 54, ... the common ratio is:
Select all linear functions.
For y(n) = 5·3^n, the value at n = 0 equals ____.
Select all sequences that are exponential (with nontrivial base b ≠...
If successive ratios y_{n+1}/y_n are equal for all n (and y_n ≠ 0),...
Which function models “starting at 50 and growing by 8% per day”?
A linear model can represent decrease using a negative slope.
A quantity has values 100, 90, 80, 70 at t = 0,1,2,3. Which model...
A quantity has values 200, 160, 128, 102.4 at t = 0,1,2,3. Which model...
The function y = 500(1.02)^t adds 2 units each time step.
Which function has a constant percent rate of change?
Identify the model: y = 7 − 0.4x.
Select all true statements about linear vs exponential change.
Consider values 5, 8, 12, 18 at t = 0,1,2,3. Which model fits best?
For y = 2.5x + 7, the amount added each time x increases by 1 is ____.
For the sequence 7, 10, 13, 16, ... the common difference is ____.
Find the common ratio for 240, 180, 135, 101.25, ...
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