Exponential Growth and Decay Functions

Front

What is exponential growth?

Back

Exponential growth occurs when the increase in a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Front

What is exponential decay?

Back

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.

Front

What does the 'a' value represent in an exponential function of the form y = a(b^x)?

Back

The 'a' value represents the initial value or starting amount before any growth or decay occurs.

Front

What is the formula for calculating compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time in years.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

How do you calculate the population after a certain number of months with exponential growth?

Back

Use the formula P = P0(1 + r)^t, where P0 is the initial population, r is the growth rate, and t is the time in months.

Front

What is the decay rate in an exponential decay function of the form y = a(b^x)?

Back

The decay rate is calculated as (1 - b), where b is the base of the exponential function.

Front

If a population of 4000 grows at a rate of 25% per month, how many will there be after 4 months?

Back

9765

Front

What is the horizontal asymptote of the function y = 3(2^x)?

Back

The horizontal asymptote is the x-axis.

Front

How much will $1500 grow in an account with 4% interest compounded monthly after 6 years?

Back

$1906.11