A1 M5 D4 Flashcard 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. It describes growth or decay processes.

Front

How do you write an equation for a quantity that triples every day?

Back

The equation is y = a(3)^x, where 'a' is the initial amount and 'x' is the number of days.

Front

What does the term 'initial value' mean in an exponential function?

Back

The initial value is the starting amount before any growth or decay occurs, represented by 'a' in the function f(x) = a(b)^x.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.

Front

How do you evaluate an exponential function at a specific value?

Back

To evaluate an exponential function, substitute the value of 'x' into the function and calculate the result.

Front

What is the general form of an exponential growth equation?

Back

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

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 find the value of an exponential function at t=3?

Back

Substitute t=3 into the function and calculate the result using the equation provided.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

How can you represent a situation where a quantity decreases by a factor of 1/3 each day?

Back

The equation is y = a(1/3)^x, where 'a' is the initial amount and 'x' is the number of days.