Exponential Function Calculator

This tool works with exponential functions written as f(x) = a raised to the power bx + c, plus d. Enter the four parameters and it evaluates the function at a point, solves the equation for x, or turns a growth rate into a doubling time and a half life. A fourth mode fits the one exponential curve that passes through two readings and reports the rate between them, and a fifth solves equations with a power on both sides or a coefficient in front, such as 2^(x+1) = 3^(x-2) or 5 * 2^x = 40, step by step with natural logs. There is no expression parsing, so the shape of the function is fixed and every answer is a closed form rather than a numerical search.

Calculator Type
A base above 1 grows, a base between 0 and 1 decays. Use 2.718281828 for e.
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A base above 1 grows, a base between 0 and 1 decays. Use 2.718281828 for e.
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Leave the right-hand base at 1 for an equation like 5 * 2^x = 40, where one side is a plain number.

The number multiplying the left power. 1 if there is none.
A base above 1 grows, a base between 0 and 1 decays. Use 2.718281828 for e.
The number multiplying the right power, or the whole right side when its base is 1.
Leave at 1 when the right side is just the number m.
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For a quantity that changes by a fixed percentage each period.

Positive for growth, negative for decay. 7 means the quantity is multiplied by 1.07 each period.
How many times the starting amount you want to reach. Use a value below 1 for decay, such as 0.125.
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Two readings of the same quantity determine one exponential curve y = A * r^x.

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