Exponential Growth and Decay

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

Front

What is the formula for exponential growth?

Back

The formula is y = a(1 + r)^t, where 'a' 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 y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

How do you calculate the value of an asset after depreciation?

Back

Use the formula: Final Value = Initial Value * (1 - Decay Rate)^t.

Front

What is the significance of the decay rate in depreciation?

Back

The decay rate indicates how quickly an asset loses value over time, affecting its future worth.

Front

If a printer costs $35,000 and depreciates at 5% per year, what will its value be after 8 years?

Back

$23,219.72.

Front

If land is purchased for $30,000 and appreciates at 5% per year, what will its value be after 51 years?

Back

$344,022.

Front

What is the future value of a $3,000 deposit in a savings account with 4% interest after 10 years?

Back

$4,440.73.

Front

What is the exponential equation for a car worth $15,000 depreciating at 8% per year?

Back

y = 15,000(0.92)^x.