Exponential Functions

Front

What is an exponential function?

Back

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

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is y = a * b^x, where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is y = a * b^x, where 0 < b < 1.

Front

How do you determine if an exponential function represents growth or decay?

Back

If the base 'b' of the exponential function is greater than 1, it represents growth. If 'b' is between 0 and 1, it represents decay.

Front

What is the range of the function y = 2^(x+1) - 3?

Back

The range of the function y = 2^(x+1) - 3 is (-3, ∞).

Front

What does the term 'asymptote' refer to in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is typically the line y = k, where k is a constant.

Front

What is the effect of changing the base 'b' in an exponential function?

Back

Changing the base 'b' affects the rate of growth or decay. A larger base results in faster growth, while a smaller base (greater than 0 but less than 1) results in faster decay.

Front

How can you express the depreciation of an asset using an exponential function?

Back

Depreciation can be expressed using the formula y = a(1 - r)^x, where 'a' is the initial value, 'r' is the rate of depreciation, and 'x' is the time in years.

Front

What is the value of a car that depreciates at a rate of 8% per year if its initial value is $15,000?

Back

The value of the car after x years can be expressed as y = 15,000(0.92)^x.

Front

What is the significance of the y-intercept in an exponential function?

Back

The y-intercept of an exponential function is the value of y when x = 0, which is equal to the constant 'a' in the function y = a * b^x.