Identifying geometric (exponential) number patterns and tables for y = a*b^x + c

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Learning objective overview

Master Teaching Guide coverage for this objective.

Dr Austin Maths - Generating Different Types of Sequence Practice GridQuestions PDF · Answers
Dr Austin Maths - Geometric Sequences Practice GridQuestions PDF · Answers

Continue a geometric (exponential) sequence and identify its multiplier (common ratio).
Distinguish exponential sequences from linear or quadratic sequences by testing for a common ratio versus a common difference.
Complete a table of values for y = b^x and for transformed forms y = a·b^x + c.
Identify growth (ratio greater than 1) or decay (ratio between 0 and 1) from a table of values or an equation.
Read the y-intercept and horizontal asymptote directly from an exponential equation, and use them together with growth/decay to describe or compare graphs.
Derive an exponential rule a·b^x + c from a table of values or from a described starting value and growth/decay factor.
Solve for an unknown coefficient a in a rule y = a·b^x + c given one point the graph passes through.

Extends identifying/extrapolating exponential patterns (T4_LO1, T4_LO2 -- exponential patterns have a common ratio rather than a common difference) into building a table of values for y = a*b^x + c and reading off features from it.
This page's task decks (OBJECTIVES/lo-exponential-patterns-and-graphs) cover: continuing a geometric sequence and naming its multiplier (common ratio); distinguishing exponential from linear sequences; completing tables of values for y = b^x and transformed forms y = a*b^x + c; identifying growth (ratio greater than 1) vs decay (ratio between 0 and 1) from a table; reading the y-intercept and horizontal asymptote directly from the equation; and, at excellence tier, deriving the rule a*b^x + c from a table or from a described starting value and growth/decay factor, including solving for an unknown coefficient a given one point.
Distinguish this page from the separate 'Drawing exponential graphs' page (T4_EX04, a different native extension): that page's task decks are purely about plotting/sketching y = b^x style graphs by hand, whereas this page is about the numeric pattern/table/rule side (no plotting).