Exponential Flashcard 12.13.24

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Back

Front

If a car depreciates in value by 7% each year, what is the formula to calculate its value after 't' years?

Back

Value = Initial Value * (1 - Depreciation Rate)^t

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Back

Front

What is the formula for exponential decay?

Back

N(t) = N_0 * e^{-kt}, where N_0 is the initial quantity, k is the decay constant, and t is time.

Front

A population of fish starts at 8,000 and decreases by 6% per year. What is the formula to find the population after 't' years?

Back

Population = Initial Population * (1 - 0.06)^t

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Back

Front

What does it mean for a quantity to decrease by a percentage?

Back

It means that the quantity is multiplied by (1 - percentage) each time period.

Front

If Mr. Hoffner bought a Jeep for $40,000 and it depreciates by 7% per year, what is the value after 1 year?

Back

Value after 1 year = 40000 * (1 - 0.07) = $37,200.

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Back

Front

If a quantity decreases by 10% each year, what is the value after 3 years if it starts at 100?

Back

Value = 100 * (1 - 0.10)^3 = 100 * 0.729 = 72.9.