Algebra 2 - Week 04/06-04/10 - Exponential Growth and Decay

Front

What is the growth factor in an exponential growth function?

Back

The growth factor is the base of the exponential function, representing the rate of increase. For example, in the function y = a(1 + r)^x, the growth factor is (1 + r).

Front

How do you model exponential decay in a function?

Back

Exponential decay can be modeled using the function f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

Front

What does the equation y = 720,500(1.022)^x represent?

Back

This equation models the population growth of Brownville, where 720,500 is the initial population and 1.022 is the growth factor per year.

Front

How do you calculate the total amount paid on a loan with compound interest?

Back

Use the formula A = P(1 + r/n)^(nt), where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the initial amount in the function y = 15(1.35)^x?

Back

The initial amount is $15, which is the value of y when x = 0.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time period.

Front

What does a growth rate of 35% mean in an exponential function?

Back

A growth rate of 35% means that the quantity increases by 35% of its current value each time period.

Front

How do you determine the population after a certain number of years using an exponential model?

Back

Substitute the number of years into the model equation to find the population at that time.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth increases over time, while exponential decay decreases over time.

Front

How can you express a decrease of 14.9% in a function?

Back

A decrease of 14.9% can be expressed as f(x) = a(1 - 0.149)^x.