OCR C1 — Question 6

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
TopicExponential Functions

6. (a) Given that \(y = 2 ^ { x }\), find expressions in terms of \(y\) for
  1. \(2 ^ { x + 2 }\),
  2. \(2 ^ { 3 - x }\).
    (b) Show that using the substitution \(y = 2 ^ { x }\), the equation $$2 ^ { x + 2 } + 2 ^ { 3 - x } = 33$$ can be rewritten as $$4 y ^ { 2 } - 33 y + 8 = 0$$ (c) Hence solve the equation $$2 ^ { x + 2 } + 2 ^ { 3 - x } = 33$$