Exponential Growth and Decay

Front

What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase. Example: A population that doubles every year.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease. Example: A radioactive substance that loses half of its mass every year.

Front

What is the formula for Exponential Growth?

Back

The formula is A = P(1 + r)^t, where A is the amount after time t, P is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for Exponential Decay?

Back

The formula is A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is time.

Front

What does the variable 'b' represent in the function f(x) = P(b)^x?

Back

The variable 'b' represents the base or common ratio, indicating the growth (b > 1) or decay (0 < b < 1) factor.

Front

If Jack invests $600 at a 5% interest rate, how much will he have after 5 years?

Back

$765.77

Front

Classify the model A=1200(0.85)^6 as Exponential GROWTH or DECAY.

Back

Decay

Front

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

Back

Growth

Front

Which function shows an initial amount of $15 and an increase of 35% each year?

Back

y = 15(1.35)^x

Front

What is the initial amount in the function A = 500(1.2)^t?

Back

The initial amount is $500.