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Exponential equationsAlgebraHigh schoolabout 1:10

Solve 100 * 1.05^x = 200: animated lesson

A narrated, step-by-step exponential equations video lesson with captions. Final answer: x ≈ 14.20669908.

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.4 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Solving an equation
    100⋅1.05x=200100\cdot{1.05}^{ x} = 200
  2. 2. Step by step
    1. 100⋅1.05x=200100\cdot{1.05}^{ x} = 200
      Start with the equation
    2. f(x)=100⋅21x20x−200=0f(x) = \frac{100\cdot{21}^{ x}}{{20}^{ x}}-200 = 0
      Rewrite as f(x) = 0
    3. This equation is not polynomial, so solve it numerically
    4. x≈14.20669908x \approx 14.20669908
      Found 1 solution in [−10⁹, 10⁹]
  3. 3. The answer
    x ≈ 14.20669908\text{x ≈ 14.20669908}

    x ≈ 14.20669908

  4. 4. Check
    • x = 14.206699: left side = 200, right side = 200 ✓

Transcript

The problem. Here is the problem: 100 times 1.05 to the power x equals 200. Solve for x numerically (the equation contains functions such as sin, log or roots).

Step by step. Start with the equation. Rewrite as f(x) equals 0. This equation is not polynomial, so solve it numerically. Scan x from negative 10 to the power 9 to 10 to the power 9 for sign changes of f and for points where the graph touches the axis, then narrow each one down. Every root is checked by substituting it back. Found 1 solution in [−10 to the power 9, 10 to the power 9].

The answer. So the answer is x approximately 14.20669908. Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

Check. x equals 14.206699: left side equals 200, right side equals 200, which checks out.

About exponential equations

Solve equations with the variable in the exponent using logarithms.

More lessons like this

Solve 100 * 1.05^x = 200: Animated Step-by-Step Lesson