Exponential Function Practice

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

Back

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

Front

What is the base in an exponential function?

Back

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

Front

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

Back

To find the y-intercept, substitute x = 0 into the function and solve for y.

Front

What is the multiplier in an exponential decay situation?

Back

The multiplier is the remaining percentage of the quantity after each time period, expressed as a decimal. For example, if 30% dies, the multiplier is 0.7.

Front

If a culture of bacteria decreases by 30% each year, what is the equation representing this situation?

Back

y = 5000(0.7^x), where 5000 is the initial amount and 0.7 is the multiplier.

Front

What does a negative exponent indicate in an exponential function?

Back

A negative exponent indicates a reciprocal. For example, b^(-x) = 1/(b^x).

Front

What is the general form of an exponential growth function?

Back

The general form is y = a(b^x), where 'a' is the initial amount and 'b' is the growth factor.

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

How do you express a percentage decrease as a decimal multiplier?

Back

To express a percentage decrease, subtract the percentage from 100% and convert it to a decimal. For example, a 30% decrease is 1 - 0.30 = 0.70.