Alg Module 11 and 12 Review Flashcard

Front

What does the expression 12(1.015)^t represent in terms of population growth?

Back

It models the population of elephants in a wildlife refuge after t years since 1975, indicating that the population is increasing.

Front

What type of function is represented by f(x)=2(1/7)^x?

Back

Exponential Decay.

Front

What is an asymptote in a graph?

Back

An asymptote is a line that a graph approaches but never touches. For example, y = 2 is a horizontal asymptote.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values). For example, if the range is y > -6, it means all values greater than -6 are included.

Front

How can you determine if a population is increasing or decreasing from an exponential model?

Back

If the base of the exponential function is greater than 1, the population is increasing. If it is between 0 and 1, the population is decreasing.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases over time, while exponential decay occurs when a quantity decreases over time.

Front

What does the term 'exponential function' refer to?

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, and 'x' is the exponent.

Front

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

Back

The base determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

How do you identify 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 general form of an exponential growth function?

Back

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