4024/22 May/Jun 2023, Question 4: Exponential Functions

Part (a) · 1 mark

Fill in the missing y-value in the table for y = 2ˣ/5 at x = 4.

1. 1y = 2⁴/5 = 16/5 = 3.2

Answer3.2

Part (b) · 3 marks

Plot the curve y = 2ˣ/5 on the grid for x from −1 to 4.

1. 1Plot (−1, 0.1), (0, 0.2), (1, 0.4), (2, 0.8), (3, 1.6), (4, 3.2)
2. 2Join with a smooth curve

AnswerCorrect smooth curve

Part (c) · 2 marks

Sketch the curve, add a straight line to the grid, and use it to solve 2ˣ = 6.

1. 12ˣ = 6 means 2ˣ/5 = 6/5 = 1.2
2. 2Draw the line y = 1.2 and read x where it meets the curve
3. 3x ≈ 2.6 (exact value 2.58…)

Answer2.5 to 2.7

Part (di) · 1 mark

Fill in the two missing y-values in the table for 4y = 2x + 1 at x = −1 and x = 2.

1. 1x = −1: 4y = −2 + 1 = −1, y = −0.25
2. 2x = 2: 4y = 4 + 1 = 5, y = 1.25

Answer−0.25, 1.25

Part (dii) · 1 mark

Add the straight line 4y = 2x + 1 to the same grid, for −1 ≤ x ≤ 4.

1. 1Plot (−1, −0.25), (2, 1.25), (4, 2.25)
2. 2Rule a straight line from (−1, −0.25) to (4, 2.25)

AnswerRuled line from (−1, −0.25) to (4, 2.25)

Part (diii) · 1 mark

Read off the x-coordinates where the line 4y = 2x + 1 meets the curve y = 2ˣ/5.

1. 1Read the x-coordinates where the line meets the curve
2. 2x ≈ −0.14 and x ≈ 3.2

Answer−0.25 to −0.05, 3.1 to 3.3

Part (div) · 3 marks

Combine the two equations to form A × 2ˣ + Bx + C = 0 and state the integer values of A, B and C.

1. 1From the line: y = (2x + 1)/4
2. 22ˣ/5 = (2x + 1)/4
3. 34 × 2ˣ = 5(2x + 1) = 10x + 5
4. 44 × 2ˣ − 10x − 5 = 0
5. 5A = 4, B = −10, C = −5

AnswerA = 4, B = −10, C = −5 OR A = −4, B = 10, C = 5

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