Exponential Functions Word Problems

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What is an exponential function?

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An exponential function is a mathematical function of the form y = a(b)^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It represents growth or decay processes.

Front

What does it mean for a value to depreciate?

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Depreciation refers to the reduction in the value of an asset over time, often due to wear and tear or obsolescence.

Front

What is the formula for calculating depreciation?

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

Front

What is the growth factor in exponential growth?

Back

The growth factor is the amount by which a quantity increases in each time period, represented as (1 + r), where r is the growth rate.

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What is the decay factor in exponential decay?

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The decay factor is the amount by which a quantity decreases in each time period, represented as (1 - r), where r is the decay rate.

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How do you express a 25% depreciation in terms of a decay factor?

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A 25% depreciation can be expressed as a decay factor of 0.75, since 1 - 0.25 = 0.75.

Front

What is the initial value in a word problem?

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The initial value is the starting amount before any growth or decay occurs, often represented by 'a' in the exponential function.

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How do you write an exponential growth equation?

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An exponential growth equation can be written in the form y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the difference between growth rate and growth factor?

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The growth rate is the percentage increase (r), while the growth factor is the multiplier used in calculations (1 + r).

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What is the formula for calculating the future value of an investment with exponential growth?

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The formula is A = P(1 + r)^t, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, and t is the number of years.