Exponential Word Problems

Front

What is an exponential decay function?

Back

An exponential decay function describes a situation where a quantity decreases at a rate proportional to its current value, often represented as y = a * e^(-kt), where 'a' is the initial amount, 'k' is the decay constant, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

What is an exponential growth function?

Back

An exponential growth function describes a situation where a quantity increases at a rate proportional to its current value, often represented as y = a * e^(kt), where 'a' is the initial amount, 'k' is the growth constant, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

To calculate the future value of an investment with exponential growth, use the formula: Future Value = Present Value * (1 + r)^t, where 'r' is the growth rate and 't' is the number of time periods.

Front

How do you calculate the future value of an asset with exponential decay?

Back

To calculate the future value of an asset with exponential decay, use the formula: Future Value = Present Value * (1 - r)^t, where 'r' is the decay rate and 't' is the number of time periods.

Front

What is the significance of the decay rate in exponential decay problems?

Back

The decay rate indicates how quickly the quantity decreases over time. A higher decay rate results in a faster decrease in value.

Tags

CCSS.HSF-IF.C.8B

Front

What is the significance of the growth rate in exponential growth problems?

Back

The growth rate indicates how quickly the quantity increases over time. A higher growth rate results in a faster increase in value.

Tags

CCSS.HSF-IF.C.8B

Front

What is the doubling time in exponential growth?

Back

Doubling time is the period it takes for a quantity to double in size, often calculated using the rule of 70: Doubling Time (in years) = 70 / growth rate (as a percentage).

Front

What is the half-life in exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value, commonly used in contexts like radioactive decay.

Tags

CCSS.HSF-LE.A.1C

Front

How do you interpret the results of exponential growth and decay in real-world scenarios?

Back

Exponential growth and decay can model various real-world phenomena, such as population growth, financial investments, and depreciation of assets.

Front

What is the formula for continuous compounding in finance?

Back

The formula for continuous compounding is A = Pe^(rt), where 'A' is the amount of money accumulated after time 't', 'P' is the principal amount, 'r' is the annual interest rate, and 'e' is Euler's number.