MCLA - 7.3-7.5 - Exponential Functions

Front

What is an exponential function?

Back

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

Front

What does the base of an exponential function represent?

Back

The base of an exponential function represents the growth (if greater than 1) or decay (if between 0 and 1) factor of the function.

Front

How do you find the y-intercept of an exponential function?

Back

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

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

If a quantity decreases by 30% each hour, what is the decay factor?

Back

The decay factor is 1 - 0.30 = 0.70.

Front

How do you calculate the remaining amount after multiple hours of decay?

Back

To calculate the remaining amount after multiple hours of decay, use the formula f(t) = a(d)^t, where 'd' is the decay factor.

Front

What does the initial value represent in an exponential function?

Back

The initial value represents the starting amount before any growth or decay occurs.

Front

In the function f(x) = 800(0.87)^x, what does 0.87 represent?

Back

The value 0.87 represents the decay factor, indicating that the quantity decreases by 13% each time period.

Front

What is the relationship between exponential functions and their graphs?

Back

Exponential functions have graphs that are continuous and either increase rapidly (growth) or decrease rapidly (decay) as x moves away from zero.