Exponential Word Problems

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What is an exponential function?

Back

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

Front

What does it mean for a quantity to double?

Back

Doubling means that the quantity increases to twice its original amount. In exponential growth, this often occurs at regular intervals.

Front

How do you calculate the population after a certain number of years with a growth rate?

Back

Use the formula P = P0 * (1 + r)^t, where P0 is the initial population, r is the growth rate (as a decimal), and t is the number of years.

Front

What is the formula for calculating compound interest?

Back

The formula is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

If a population increases by 15% each year, what is the growth factor?

Back

The growth factor is 1.15, which represents the original population plus the 15% increase.

Front

How do you find the future value of an investment with a percentage decrease?

Back

Use the formula V = V0 * (1 - r)^t, where V0 is the initial value, r is the decrease rate (as a decimal), and t is the time period.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, leading to faster increases over time, while linear growth increases by a constant amount.

Front

How do you solve an exponential equation?

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To solve an exponential equation, you can take the logarithm of both sides, which allows you to bring down the exponent and solve for the variable.

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What is a decay factor in exponential decay problems?

Back

The decay factor is calculated as (1 - r), where r is the decay rate. It represents the fraction of the quantity that remains after each time period.

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How do you express a percentage increase as a decimal?

Back

To express a percentage increase as a decimal, divide the percentage by 100. For example, a 20% increase is expressed as 0.20.