CW#29 - Exponential Word Problems

Front

What is an exponential growth model?

Back

An exponential growth model describes a situation where a quantity increases at a rate proportional to its current value, often represented by the equation y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is time.

Front

What is an exponential decay model?

Back

An exponential decay model describes a situation where a quantity decreases at a rate proportional to its current value, often represented by the equation y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is time.

Front

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

Back

Use the formula: Future Value = Present Value * (1 + r)^t, where 'r' is the growth rate and 't' is the time in years.

Front

How do you calculate the present value of a depreciating asset?

Back

Use the formula: Present Value = Future Value / (1 - r)^t, where 'r' is the depreciation rate and 't' is the time in years.

Front

What does the term 'growth rate' mean in exponential functions?

Back

The growth rate is the percentage increase in a quantity over a specific period, often expressed as a decimal in the exponential function.

Front

What is the formula for calculating population growth?

Back

The formula for population growth is P(t) = P0 * e^(rt), where P0 is the initial population, r is the growth rate, and t is time.

Front

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

Back

The base in an exponential function determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

How do you determine the value of an asset after a certain number of years of depreciation?

Back

Use the formula: Value = Initial Value * (1 - r)^t, where 'r' is the depreciation rate and 't' is the number of years.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount over time, while exponential growth increases by a percentage of the current value, leading to faster growth as time progresses.

Front

How do you express a 14% growth rate as a decimal?

Back

To express a 14% growth rate as a decimal, divide by 100: 14% = 0.14.