Exponential Growth & Decay + Compound Interest

Front

What does the 'r' stand for in the formula for exponential growth?

Back

Rate

Front

Write an equation that models the following situation: Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

Back

y=6(1.14)^{x}

Front

Classify the model A=10(1.01)^{3} as Exponential GROWTH or DECAY.

Back

Growth

Front

What is the formula for exponential growth?

Back

f(x)=a(1+r)^{x}

Front

Is y = 4(0.20)^{x} growth or decay?

Back

Decay

Front

Define 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.

Front

Define Exponential Decay.

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a rapid decrease that slows over time.

Front

What is the formula for compound interest?

Back

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

Front

If a population of bacteria doubles every 3 hours, what is the growth factor?

Back

The growth factor is 2.

Front

What is the difference between simple interest and compound interest?

Back

Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal and also on the accumulated interest.