Exponential Word Problems

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What is exponential decay?

Back

Exponential decay is a decrease in a quantity by a consistent percentage over a period of time, often modeled by the function f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

Front

What is exponential growth?

Back

Exponential growth is an increase in a quantity by a consistent percentage over a period of time, often modeled by the function f(x) = a(1 + r)^x, where 'a' is the initial amount and 'r' is the growth rate.

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What does depreciation mean in finance?

Back

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

Front

How do you express a 5% depreciation rate in a function?

Back

A 5% depreciation rate can be expressed as f(x) = a(0.95)^x, where 'a' is the initial value.

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What is the formula for calculating the remaining value of an asset after depreciation?

Back

The formula is f(x) = a(1 - r)^x, where 'a' is the initial value, 'r' is the depreciation rate, and 'x' is the number of years.

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What is the initial value in an exponential function?

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The initial value is the starting amount before any growth or decay occurs, represented by 'a' in the function f(x) = a(1 + r)^x or f(x) = a(1 - r)^x.

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How do you convert a percentage growth rate to a decimal for calculations?

Back

To convert a percentage growth rate to a decimal, divide the percentage by 100. For example, 14% becomes 0.14.

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What is the significance of the base in an exponential function?

Back

The base in an exponential function determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

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How do you write an equation for a quantity that grows by 14% each week?

Back

The equation is y = a(1.14)^x, where 'a' is the initial quantity and 'x' is the number of weeks.

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What does it mean if a quantity decreases by 12% per day?

Back

It means that each day, the quantity retains 88% of its value, which can be expressed as y = a(0.88)^t.