Exponential Functions Word Problems

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 it mean for a value to depreciate?

Back

Depreciation refers to the reduction in the value of an asset over time, often due to wear and tear or obsolescence.

Tags

CCSS.RI.11-12.5

CCSS.RI.8.3

CCSS.RI.8.5

CCSS.RI.9-10.3

CCSS.RI.9-10.5

Front

What is the formula for calculating depreciation?

Back

The formula for depreciation is V = P(1 - r)^t, where V is the value after t years, P is the initial value, r is the depreciation rate, and t is the time in years.

Front

What is the growth factor in exponential growth?

Back

The growth factor is the amount by which a quantity increases in each time period, represented as (1 + r), where r is the growth rate.

Tags

CCSS.HSF-IF.C.8B

Front

What is the decay factor in exponential decay?

Back

The decay factor is the amount by which a quantity decreases in each time period, represented as (1 - r), where r is the decay rate.

Tags

CCSS.HSF-IF.C.8B

Front

How do you express a 25% depreciation in terms of a decay factor?

Back

A 25% depreciation can be expressed as a decay factor of 0.75, since 1 - 0.25 = 0.75.

Tags

CCSS.HSF-IF.C.8B

Front

What is the initial value in a word problem?

Back

The initial value is the starting amount before any growth or decay occurs, often represented by 'a' in the exponential function.

Front

How do you write an exponential growth equation?

Back

An exponential growth equation can be written in the form y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Tags

CCSS.HSF-LE.A.1A

Front

What is the difference between growth rate and growth factor?

Back

The growth rate is the percentage increase (r), while the growth factor is the multiplier used in calculations (1 + r).

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for calculating the future value of an investment with exponential growth?

Back

The formula is A = P(1 + r)^t, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, and t is the number of years.