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About Exponential Functions & Growth — Class 10 IB

Analyze exponential growth and decay models; graph exponential functions. This topic is part of the IB Class 10 mathematics syllabus (chapter: Unit 12). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Exponential Functions & Growth — solved examples for Class 10 IB

Example 1easy

Consider the following sets of (x, y) values. Which set most likely represents an exponential function?
  1. A)A: (0, 2), (1, 4), (2, 6), (3, 8)
  2. B)B: (0, 3), (1, 6), (2, 12), (3, 24)
  3. C)C: (0, 5), (1, 4), (2, 3), (3, 2)
  4. D)D: (0, 1), (1, 1), (2, 1), (3, 1)

Step-by-step solution

  1. For an exponential function, the ratio of consecutive y-values (y_n / y_{n-1}) should be constant when x-values are spaced equally.

Answer: B: (0, 3), (1, 6), (2, 12), (3, 24)

Example 2medium

A principal amount of ₹50,000 is invested at an annual interest rate of 8% compounded annually. What will be the total amount accumulated after 3 years?
  1. A)₹62,985.60
  2. B)₹60,000.00
  3. C)₹65,340.00
  4. D)₹58,320.00

Step-by-step solution

  1. Identify the given values: Principal (P) = ₹50,000, Rate (r) = 8% = 0.08, Time (t) = 3 years.
  2. Apply the compound interest formula: A = P(1 + r)^t.
  3. Substitute the values: A = 50000(1 + 0.08)^3.
  4. Calculate the amount: A = 50000(1.08)^3 = 50000 × 1.259712 = ₹62,985.60.

Answer: ₹62,985.60

Example 3hard

An exponential function f(x) = k × a^(x+m) + n, where k > 0, has a domain of all real numbers and a range of (2, ∞). The y-intercept is (0, 7). Which of the following statements must be true?
  1. A)k = 5
  2. B)n = 2
  3. C)a < 0
  4. D)m = 0

Step-by-step solution

  1. For an exponential function of the form f(x) = k × a^(x+m) + n, the horizontal asymptote is y = n. Since k > 0, the term k × a^(x+m) is always positive (assuming a > 0, which is standard for exponential bases).
  2. Therefore, f(x) > n. Given that the range is (2, ∞), it means the values of f(x) are always greater than 2. This implies that the horizontal asymptote is y = 2.
  3. Thus, n must be equal to 2.
  4. The y-intercept (0, 7) means f(0) = 7. So, k × a^(0+m) + 2 = 7, which simplifies to k × a^m = 5. While this gives a relationship between k, a, and m, we cannot determine their individual values from the given information alone. However, n = 2 is definitively true.

Answer: n = 2

Practice questions on Exponential Functions & Growth

  1. Q1.easy

    Which of the following exponential functions represents exponential decay?
    1. A)A: f(x) = 3 × (1.5)^x
    2. B)B: g(x) = 0.5 × (2)^x
    3. C)C: h(x) = 2 × (0.8)^x
    4. D)D: k(x) = 4 × (1)^x
    Show answer

    Answer: C: h(x) = 2 × (0.8)^x

    Hint: The base 'b' in an exponential function y = a × b^x determines whether it represents growth or decay. Consider the range of 'b' for each type.

  2. Q2.easy

    A new species of bacteria is discovered. It starts with an initial population of 50 cells and doubles every hour. Which of the following functions models its population P(t) after 't' hours?
    1. A)A: P(t) = 50 + 2t
    2. B)B: P(t) = 2 × (50)^t
    3. C)C: P(t) = 50 × (2)^t
    4. D)D: P(t) = 50 × (t)^2
    Show answer

    Answer: C: P(t) = 50 × (2)^t

    Hint: In the general exponential form P(t) = a × b^t, 'a' represents the initial amount and 'b' represents the growth factor per unit of time.

  3. Q3.easy

    Consider the graph of the function f(x) = 7 × (0.6)^x. Which statement about its horizontal asymptote is correct?
    1. A)A: The horizontal asymptote is at y = 7.
    2. B)B: The horizontal asymptote is at y = 0.
    3. C)C: The horizontal asymptote is at x = 0.
    4. D)D: The function has no horizontal asymptote.
    Show answer

    Answer: B: The horizontal asymptote is at y = 0.

    Hint: For a basic exponential function of the form y = a × b^x (without any vertical shifts), consider what happens to the y-values as x approaches positive or negative infinity.

  4. Q4.medium

    A new car is purchased for ₹8,00,000. Its value depreciates by 15% each year. What will be the value of the car after 2 years?
    1. A)₹5,78,000
    2. B)₹6,12,000
    3. C)₹6,80,000
    4. D)₹5,20,000
    Show answer

    Answer: ₹5,78,000

    Hint: For depreciation, the formula is A = P(1 - r)^t, where 'r' is the annual depreciation rate.

  5. Q5.medium

    Which of the following statements is TRUE regarding the exponential function f(x) = 3 × (0.5)^x?
    1. A)The function represents exponential growth.
    2. B)The y-intercept is (0, 0.5).
    3. C)The horizontal asymptote is y = 3.
    4. D)The range of the function is y > 0.
    Show answer

    Answer: The range of the function is y > 0.

    Hint: Consider the base 'b' to determine growth/decay, the value 'a' for the y-intercept, and the inherent properties of exponential functions regarding asymptotes and range.

  6. Q6.medium

    An exponential function's graph passes through the point (0, 5) and continuously decreases, approaching the x-axis as x increases. Which of the following equations could represent this function?
    1. A)y = 5 × (2)^x
    2. B)y = 5 × (0.8)^x
    3. C)y = 2 × (5)^x
    4. D)y = 0.8 × (5)^x
    Show answer

    Answer: y = 5 × (0.8)^x

    Hint: The y-intercept gives the initial value 'a', and a continuously decreasing graph indicates exponential decay, meaning the base 'b' must be between 0 and 1.

  7. Q7.hard

    The graph of y = 3^x is reflected across the x-axis, then shifted 2 units to the left, and finally shifted 4 units up. The resulting function is f(x). If f(x) passes through the point (p, 1), what is the value of p?
    1. A)-1
    2. B)1
    3. C)3
    4. D)5
    Show answer

    Answer: -1

    Hint: Apply each transformation step-by-step to the original function to find f(x). Then, substitute the point (p, 1) into the derived function.

  8. Q8.hard

    If 3^x = 5 and 5^y = 9, what is the value of xy?
    1. A)1
    2. B)2
    3. C)3
    4. D)4
    Show answer

    Answer: 2

    Hint: Try substituting one exponential expression into the other. Remember the power of a power rule for exponents: (a^m)^n = a^(mn).

  9. Q9.hard

    A bacterial culture doubles every 'h' hours. If it grows from an initial population P₀ to 8 × P₀ in 4 hours, how long will it take to grow from P₀ to 16 × P₀?
    1. A)16/3 hours
    2. B)5 hours
    3. C)20/3 hours
    4. D)6 hours
    Show answer

    Answer: 16/3 hours

    Hint: First, use the given information (P₀ to 8P₀ in 4 hours) to determine the doubling period 'h'. Then, use 'h' to find the time required for P₀ to grow to 16P₀.

These are 9 of the 60 questions available for Exponential Functions & Growth. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.