Linear Exponential Patterns Quiz: Distinguishing Linear and Exponential Patterns

  • 9th Grade
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Quizzes Created: 7682 | Total Attempts: 9,547,133
| Questions: 20 | Updated: Dec 17, 2025
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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 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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5) 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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6) 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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7) 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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8) 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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9) 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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10) 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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11) 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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12) 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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13) 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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14) 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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15) 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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16) 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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17) 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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18) 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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19) A linear model can represent decrease using a negative slope.

Explanation

For y = mt + b, a negative slope m

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20) 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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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 7, 10, 13, 16, ... the common difference is ____.
For the sequence 2, 6, 18, 54, ... the common ratio is:
Select all linear functions.
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.
For y(n) = 5·3^n, the value at n = 0 equals ____.
Which function has a constant percent rate of change?
Select all sequences that are exponential (with nontrivial base b ≠...
Identify the model: y = 7 − 0.4x.
If successive ratios y_{n+1}/y_n are equal for all n (and y_n ≠ 0),...
Find the common ratio for 240, 180, 135, 101.25, ...
Which function models “starting at 50 and growing by 8% per day”?
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?
A linear model can represent decrease using a negative slope.
For y = 2.5x + 7, the amount added each time x increases by 1 is ____.
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