AA C&C Flashcard Review - Exponential Growth & 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 a constant percentage rate over time.

Front

What is exponential decay?

Back

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

Front

How do you calculate the future value in exponential growth?

Back

Future Value = Present Value * (1 + growth rate)^time.

Front

How do you calculate the future value in exponential decay?

Back

Future Value = Present Value * (1 - decay rate)^time.

Front

What is the general form of an exponential growth function?

Back

f(x) = a(1 + r)^x, where a is the initial amount and r is the growth rate.

Front

What is the general form of an exponential decay function?

Back

f(x) = a(1 - r)^x, where a is the initial amount and r is the decay rate.

Front

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

Back

9766.

Front

What type of function is f(x)=2(1/7)^x?

Back

Exponential Decay.

Front

What type of function is y = 7(5/4)^x?

Back

Exponential Growth.

Front

If a peach doubles in size every week, how would you express its size after 5 weeks?

Back

70(2)^5.