8.5-8.6 Review 2022

Front

What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a constant percentage over a period of time, resulting in a rapid increase. Example: y = a(1 + r)^t, where r is the growth rate.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a constant percentage over a period of time. Example: y = a(1 - r)^t, where r is the decay rate.

Front

How do you identify Exponential Growth or Decay from an equation?

Back

If the base of the exponent is greater than 1, it indicates growth. If the base is between 0 and 1, it indicates decay.

Front

What does the equation y = 1200(0.85)^t represent?

Back

This equation represents Exponential Decay, as the base (0.85) is less than 1.

Front

What is the percentage increase in a population modeled by y = 800(1.07)^x?

Back

The population is increasing by 7% per time unit.

Front

What is the formula for calculating the future value of an investment with annual interest?

Back

The formula is y = P(1 + r)^t, where P is the principal amount, r is the annual interest rate, and t is the time in years.

Front

What is the exponential model for a savings account with $1500 and 1.5% interest?

Back

The model is y = 1500(1.015)^t.

Front

What is the domain of all Exponential Functions?

Back

The domain of all Exponential Functions is all real numbers.

Front

What does the expression 12(1.015)^t indicate about the population of elephants?

Back

It indicates that the population of elephants is increasing over time.

Front

What is the difference between a growth factor and a decay factor?

Back

A growth factor is greater than 1 (e.g., 1 + r), while a decay factor is less than 1 (e.g., 1 - r).