This worksheet connects the algebra and graphs of exponential relations, teaching students to identify growth and decay from a rule, and solve exponential equations by matching a common base. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- An exponential relation has the form y=A×bˣ, where A is the starting value (the y-intercept, at x=0) and b is the growth/decay factor.
- If b>1, the relation is growth — y increases as x increases. If 0<b<1, the relation is decay — y decreases as x increases.
- The graph of y=A×bˣ never touches the x-axis (it has a horizontal asymptote at y=0) and always passes through (0, A).
- An exponential equation like bˣ=k can be solved exactly by rewriting both sides with a common base, then equating the exponents.
- Real exponents (including fractions) are meaningful: bᵖ/ᵠ = the q-th root of b raised to the power p — this is how equations like 4ˣ=8 get a fractional solution.
What your child will practise:
- Evaluating an exponential relation y=A×bˣ at a given x-value.
- Identifying whether an exponential relation models growth or decay from its base, and read its y-intercept from A.
- Completing a table of values for an exponential relation and connect it to the shape of its graph.
- Solving an exponential equation by rewriting both sides with a common base and equating exponents.
- Formulating and solve a real-world growth or decay scenario (population, radioactive decay, compound-style change) as an exponential equation.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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