An exponential function grows by a factor, not by a step: f(x) = a·bˣ starts at a and multiplies by b each time x goes up one. These free printable worksheets ask a child to evaluate one at a value, and to work backwards to the exponent.
This is the exponential companion to the linear function sheets. Evaluating f(x) = 3·2ˣ at x = 4 is two moves in order: the power first, 2⁴ = 16, then the coefficient, 3·16 = 48 — and doing the multiply first, (3·2)⁴, is the mistake worth catching, so every step-by-step walk here does the power before the multiply.
Why this sheet works
The second level runs it backwards. Given f(x) = 3·2ˣ and that f(x) = 48, a child divides off the coefficient to get 2ˣ = 16, then asks which power of 2 lands on 16 — x = 4. That is solving an exponential equation by inspection, the idea a logarithm formalises later.
How this one works
One question from this sheet, worked through a step at a time.
Solve f(x) = 4 · 6ˣ for x when f(x) = 144
6ˣ = 144 ÷ 4=36
6² = 36→x = 2
First divide off the coefficient: 6ˣ = 144 ÷ 4 = 36.
Now ask which power of 6 is 36: 6² = 36, so x = 2.
