BR 11/8/24 Growth and Decay Word Problems

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is given by: P(t) = P0 * (1 + r)^t, where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and t is the time in years.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is given by: P(t) = P0 * (1 - r)^t, where P(t) is the population at time t, P0 is the initial population, r is the decay rate, and t is the time in years.

Front

How do you determine if a situation involves growth or decay?

Back

You can determine if a situation involves growth or decay by looking at the rate: if the rate is positive, it indicates growth; if the rate is negative, it indicates decay.

Front

What does a 75% increase in subscribers mean in terms of growth?

Back

A 75% increase means that for every 100 subscribers, there will be an additional 75 subscribers added, resulting in a total of 175 subscribers.

Front

What is the significance of the year 1985 in the context of the cell phone subscribers problem?

Back

The year 1985 is the starting point for the growth of cell phone subscribers in Mayville, providing the initial value needed to calculate future growth.

Front

How do you calculate the future value of an asset that depreciates?

Back

To calculate the future value of an asset that depreciates, use the formula: Future Value = Present Value * (1 - r)^t, where r is the depreciation rate and t is the time in years.

Front

What is the meaning of a 5% decrease in population?

Back

A 5% decrease in population means that each year, the population will reduce by 5% of its current value.

Front

How do you round a population number to the nearest whole number?

Back

To round a population number to the nearest whole number, look at the digit in the tenths place: if it is 5 or greater, round up; if it is less than 5, round down.

Front

What is the initial value of the book in the depreciation problem?

Back

The initial value of the book in the depreciation problem is $58.

Front

What is the value of the book after 8 years if it depreciates at 7% per year?

Back

The value of the book after 8 years is $32.46.