AQA · Mathematics · 8300
GCSE Maths: Types of graph: exponential
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Types of graph: exponential (Corbettmaths Video 345), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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Does the graph of y = aˣ (with a > 0) intersect the x-axis?
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No, because aˣ is always positive for all real x, so the graph never crosses or touches the x-axis.
If a point on y = 2ˣ has y-coordinate 128, what is its x-coordinate?
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x = 7, because 2⁷ = 128.
If a point on y = 5ˣ has y-coordinate 1/25, what is its x-coordinate?
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x = -2, because 5⁻² = 1/25.
Between which two consecutive integers does the solution to 2ˣ = 60 lie?
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Between 5 and 6, because 2⁵ = 32 and 2⁶ = 64.
For an exponential function y = abˣ, the value of ? represents the y-intercept.
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a
In the exponential model N = A × 2.25^(0.4t), what does the value of A represent when t = 0?
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The initial value or starting amount, because when t = 0, any exponential term equals 1, so N = A.
What type of graph is y = 0.4ˣ (where 0 < base < 1)?
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An exponential decay graph, which decreases as x increases.
If an island's bird population doubles from 2000 to 4000 in 2 years (Year 6 to Year 8), what type of growth is this?
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Exponential growth, because the population increases by a constant multiplicative factor over equal time intervals.
In the exponential formula M = 20000 × 2⁻ᵗ, what does the negative exponent indicate?
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Exponential decay; the quantity M decreases by half with each unit increase in t.
After 3 minutes in the model M = 20000 × 2⁻ᵗ, how many microplastics remain?
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2500, because M = 20000 × 2⁻³ = 20000 × (1/8) = 2500.
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