Exponential Functions Review

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 the base (a positive real number), and 'x' is the exponent.

Front

Identify the common ratio (multiplier) of the function f(x)=2(4)^x.

Back

4

Front

What does W(5)=75 mean in the context of the function W(x) where x is inches of rain?

Back

With 5 inches of rain, there are 75 wildflowers growing.

Front

What is the definition of a function?

Back

A function is a relation where every input has only ONE output.

Front

Identify the y-intercept (initial value) of the function f(x)=2(4)^x.

Back

2

Front

Use the function N = 14,000(0.96)^t. How many employees will there be after 3 years?

Back

12,386 employees.

Front

What is the base in the exponential function f(x) = 3(2)^x?

Back

2

Front

What does the term 'exponential growth' refer to?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.

Front

What is the formula for calculating the y-intercept of an exponential function?

Back

The y-intercept is found by evaluating the function at x=0, which gives f(0) = a(b)^0 = a.

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay; if the base is greater than 1, the function represents growth, and if it is between 0 and 1, it represents decay.