Exponential growth and Decay Exit Ticket

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, leading to rapid increases as the quantity grows.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to rapid decreases as the quantity shrinks.

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How do you calculate the future value of an investment with compound interest?

Back

Future Value = P(1 + r/n)^(nt), where P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

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What is the formula for exponential growth?

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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.

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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.

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What does it mean for a population to grow at a rate of 25% per month?

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It means that each month, the population increases by 25% of its current size.

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How do you find the value of a depreciating asset over time?

Back

Use the formula V(t) = P(1 - r)^t, where V(t) is the value after t years, P is the initial value, r is the depreciation rate, and t is time.

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What is the difference between linear growth and exponential growth?

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Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much larger increases over time.

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If a car depreciates at 18.5% per year, what is its value after one year?

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Value after one year = 25000(1 - 0.185) = $20,625.

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What is the significance of compounding frequency in interest calculations?

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The more frequently interest is compounded, the more interest will be earned on the initial principal and previously earned interest.