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

Front

What does the 'a' represent in the exponential function f(x) = a(b^x)?

Back

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

Front

What is the common ratio in an exponential function?

Back

The common ratio is the factor by which the function's value is multiplied as the input increases by one unit.

Front

How do you simplify the expression (3x^4)(5x^3)?

Back

15x^7

Front

What is the initial value of the function f(x) = 0.05(2^x)?

Back

0.05

Front

If f(x) = 2(3^x), what is the value of f(0)?

Back

2

Front

What is the general form of an exponential decay function?

Back

f(x) = a(b^x), where 0 < b < 1.

Front

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

Back

Set x = 0 in the function f(x) = a(b^x) to find the y-intercept, which is f(0) = a.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, while exponential decay occurs when the base 'b' is between 0 and 1.

Front

What is the formula for the exponential growth model?

Back

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