Exponential Functions Review

Front

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.

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when a quantity increases by a constant percentage over equal time intervals, resulting in a rapid increase.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a quantity decreases by a constant percentage over equal time intervals, resulting in a rapid decrease.

Front

How do you identify exponential growth or decay from a function?

Back

If the base 'b' in the function f(x) = a * b^x is greater than 1, it represents growth. If 'b' is between 0 and 1, it represents decay.

Front

What is the formula for calculating the future value in exponential growth?

Back

The future value can be calculated using the formula A = P(1 + r)^t, where A is the amount after time t, P is the principal amount, r is the growth rate, and t is the time.

Front

How do you calculate the population after a certain time with exponential growth?

Back

Use the formula P = P0 * (1 + r)^t, where P0 is the initial population, r is the growth rate, and t is the time in months or years.

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What is the formula for calculating the remaining amount in exponential decay?

Back

The remaining amount can be calculated using the formula 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 the time.

Front

If a population of 4000 mosquitoes grows at a rate of 25% per month, how many will there be after 4 months?

Back

After 4 months, there will be approximately 9765 mosquitoes.

Front

What is the initial amount and growth rate in the function y = 15(1.35)^x?

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The initial amount is $15 and the growth rate is 35% per year.

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How do you determine the time until a certain amount remains in exponential decay?

Back

To find the time until a certain amount remains, use the formula A = P(1 - r)^t and solve for t.