Free Exponential & log functions questions for IB Mathematics: Analysis & Approaches (SL & HL), part of Functions. Each question has the answer and the marking points an examiner would look for.
Generate a full Exponential & Log Functions worksheet →All Functions questionsThe number of bacteria in a culture is modelled by N(t) = 200ekt, where t is in hours. After 4 hours there are 360 bacteria.
Find the value of k.
Find the time taken for the number of bacteria to reach 1600.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.147 360 = 200e4k (M1) k = 14ln360200 (A1) k = 0.147 A1 | 3 |
| (b) | 14.2 hours 200ekt = 1600 (M1) t = ln(1600/200)k (A1) 14.2 hours A1 | 3 |
Let f(x) = 5x.
Solve f(2x) − 26f(x) + 25 = 0.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | x = 0, x = 2 recognizing a quadratic in 5x M1 (5x)2 − 26(5x) + 25 = 0 A1 factorizing M1 5x = 1 or 25 A1 x = 0, x = 2 A1 | 5 |
Let f(x) = −2e3x − 2, x ∈ ℝ.
Write down the equation of the horizontal asymptote of the graph of f.
Find f−1(x), and state its domain.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | y = −2 y = −2 A1 | 1 |
| (b) | f−1(x) = 13ln(x + 2−2), x < −2 interchanging x and y (M1) e3y = x + 2−2 (A1) 3y = ln(x + 2−2) (M1) f−1(x) = 13ln(x + 2−2) A1 domain x < −2 A1 | 5 |
The number of bacteria in a culture is modelled by N(t) = 2500ekt, where t is in hours. After 4 hours there are 6000 bacteria.
Find the value of k.
Find the time taken for the number of bacteria to reach 20000.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.219 6000 = 2500e4k (M1) k = 14ln60002500 (A1) k = 0.219 A1 | 3 |
| (b) | 9.50 hours 2500ekt = 20000 (M1) t = ln(20000/2500)k (A1) 9.50 hours A1 | 3 |
Let f(x) = 2x.
Solve f(2x) − 5f(x) + 4 = 0.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | x = 0, x = 2 recognizing a quadratic in 2x M1 (2x)2 − 5(2x) + 4 = 0 A1 factorizing M1 2x = 1 or 4 A1 x = 0, x = 2 A1 | 5 |
Let f(x) = 3e0.5x + 2, x ∈ ℝ.
Write down the equation of the horizontal asymptote of the graph of f.
Find f−1(x), and state its domain.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | y = 2 y = 2 A1 | 1 |
| (b) | f−1(x) = 2ln(x − 23), x > 2 interchanging x and y (M1) e0.5y = x − 23 (A1) 0.5y = ln(x − 23) (M1) f−1(x) = 2ln(x − 23) A1 domain x > 2 A1 | 5 |
Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.
Meet Riyaz →Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in