Exponential Regression update

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 an exponential function?

Back

The 'a' represents the y-intercept of the function, which is the value of f(x) when x = 0.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a(b^x) where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a(b^x) where 0 < b < 1.

Front

What is the asymptote of the function y = 2^(x-3)?

Back

The asymptote is y = 0.

Front

How do you determine the percentage decay in a function like f(x) = 800(0.87)^x?

Back

The percentage decay is found by subtracting the base from 1 and multiplying by 100. Here, 1 - 0.87 = 0.13, so the decay is 13%.

Front

What does the base 'b' in an exponential function indicate?

Back

The base 'b' indicates the growth or decay factor. If b > 1, the function represents growth; if 0 < b < 1, it represents decay.

Front

What is the difference between exponential growth and exponential decay?

Back

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

Front

What is the value of f(0) in the function f(x) = 1(2^x)?

Back

f(0) = 1(2^0) = 1.

Front

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

Back

The y-intercept indicates the initial value of the function when x = 0.