Exponential Functions Test

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 represents growth or decay processes.

Front

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

Back

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

Tags

CCSS.HSF.LE.B.5

Front

How do you calculate the future value of an investment using exponential growth?

Back

Future Value = Present Value * (1 + growth rate)^number of periods.

Front

What is the formula for exponential decay?

Back

Exponential decay can be modeled by the formula y = a(1 - r)^t, where 'r' is the decay rate and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

If a population grows by 25% each month, what is the growth factor?

Back

The growth factor is 1 + 0.25 = 1.25.

Tags

CCSS.HSF-LE.A.1C

Front

How do you find the value of an asset after depreciation?

Back

Value = Initial Value * (1 - depreciation rate)^number of years.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

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

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

How do you determine the number of periods in an exponential growth problem?

Back

The number of periods is typically given in the problem or can be calculated based on the time frame of growth.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula to calculate the population after a certain number of months given an initial population and growth rate?

Back

Population = Initial Population * (1 + growth rate)^number of months.