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. It shows rapid growth or decay.

Front

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

Back

The base 'b' in an exponential function determines the rate of growth or decay. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Front

Write the general form of an exponential growth function.

Back

y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time.

Front

Write the general form of an exponential decay function.

Back

y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time.

Front

What is the y-intercept of an exponential function?

Back

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

Front

Evaluate the function y = 3(2^x) at x = 2.

Back

y = 3(2^2) = 3(4) = 12.

Front

What is the value of any non-zero number raised to the power of 0?

Back

Any non-zero number raised to the power of 0 is equal to 1.

Front

Classify the model A = 500(0.9)^t as growth or decay.

Back

Decay.

Front

Classify the model A = 200(1.05)^t as growth or decay.

Back

Growth.

Front

If Samantha's hair grows at a rate of 14% per week, what is the growth factor?

Back

The growth factor is 1.14.