Exponential growth and decay/ Compound Interest1

Front

What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time. An example is population growth where the number of individuals increases rapidly.

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decrease that slows over time. An example is radioactive decay.

Front

Define compound interest.

Back

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Front

What is the formula for compound interest?

Back

The formula for compound interest is: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, 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 number of years.

Front

How do you calculate the balance after a certain number of years with compound interest?

Back

To calculate the balance, use the compound interest formula: A = P(1 + r/n)^(nt). Substitute the values for P, r, n, and t.

Front

What does it mean if a function has a decay rate of 18%?

Back

A decay rate of 18% means that the value decreases to 82% of its previous value each time period.

Front

What is the initial value in an exponential function?

Back

The initial value in an exponential function is the starting amount before any growth or decay occurs, often represented as 'a' in the function y = a(b)^x.

Front

What is the growth rate in the function f(x) = 354(1.15)^x?

Back

The growth rate is 15%, meaning the quantity increases by 15% for each time period.

Front

What is the difference between linear and exponential growth?

Back

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

Front

How do you determine if a function represents exponential growth or decay?

Back

If the base of the exponential function is greater than 1, it represents growth. If the base is between 0 and 1, it represents decay.