Exponential Functions 2

An exponential function is a mathematical function of the form $$f(x) = a \times b^x$$ , where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

The base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

The y-intercept of an exponential function $$f(x) = a \times b^x$$ is found by evaluating $$f(0)$$ , which equals 'a'.

The general form of an exponential growth function is $$f(t) = a(1 + r)^t$$ , where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

The general form of an exponential decay function is $$f(t) = a(1 - r)^t$$ , where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

The growth factor is 2, meaning the base 'b' in the exponential function is 2.

The 'a' represents the initial value or the y-intercept of the function.

Use the formula $$V = P(1 + r)^t$$ , where 'P' is the principal amount, 'r' is the rate of interest, and 't' is the time in years.

The formula for continuous exponential growth is $$N(t) = N_0 e^{rt}$$ , where 'N_0' is the initial amount, 'e' is Euler's number, 'r' is the growth rate, and 't' is time.

A negative growth rate indicates exponential decay, meaning the quantity decreases over time.