Exponential Growth and Decay

An exponential function is a function of the form y = ab^x​,

where a ≠ 0, b > 0, and b ≠ 1. The base is a constant and the exponent is a variable. Exponential functions are non-linear.

Some text here about the topic of discussion

• a is the initial or starting amount​ (y-intercept)

• b is the base and must be larger than 0 to represent growth.

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Domain: (-∞, ∞) all real numbers (never changes)

​Range: (0, ∞) or y > 0 (may change with transformations)

​Horizontal asymptote: y = 0 (changes vertical shifts in the graph)

Y-intercept: (0, 1) or (0, a)​

​y = ab^x, b > 1 and a ≠ 0

• A is the amount at a specified time.

• P is the investment or starting amount

• r is the interest rate written as a decimal.

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• t is the time

• 1 + r is the base and should be greater than 0 to represent growth

​A = P(1 + r)^t

Increases from left to right.

Y-intercept: (0, 1)

Horizontal Asymptote: y = 0​

Exponential Growth

• a is the initial or starting amount​ (y-intercept)

• b is the base and must be a decimal between 0 and 1 or a proper fractions.

​

​

Domain: (-∞, ∞) all real numbers (never changes)

​Range: (0, ∞) or y > 0 (may change with transformations)

​Horizontal asymptote: y = 0 (changes vertical shifts in the graph)

Y-intercept: (0, 1) or (0, a)​

​y = ab^x, 0 < b < 1 and a ≠ 0

• A is the amount at a specified time.

• P is the investment or starting amount

• r is the interest rate written as a decimal.

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• t is the time

• 1 - r is the base and should be a decimal between 0 and 1 or a proper fraction to represent decay

​A = P(1 - r)^t

Decreases from left to right.

Y-intercept: (0, 1)

Horizontal Asymptote: y = 0​

Exponential Decay