Exponential Word Problems

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What is an exponential function?

Back

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 shows rapid growth or decay.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value (e.g., y = a(b^x) where b > 1). Exponential decay occurs when a quantity decreases at a rate proportional to its current value (e.g., y = a(b^x) where 0 < b < 1).

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

How do you identify an exponential growth equation from a list of equations?

Back

An exponential growth equation will have a base greater than 1 in the form y = a(b^x) where b > 1.

Front

How do you identify an exponential decay equation from a list of equations?

Back

An exponential decay equation will have a base between 0 and 1 in the form y = a(b^x) where 0 < b < 1.

Front

What is the value of a car that depreciates at 8% per year after 1 year if its initial value is $15,000?

Back

The value after 1 year is $15,000(0.92) = $13,800.

Tags

CCSS.HSF.BF.A.2

Front

If a bank account earns 3.8% interest compounded annually, what is the formula to calculate the balance after 't' years?

Back

The formula is A = P(1 + r)^t, where A is the amount, P is the principal, r is the interest rate, and t is the time in years.

Front

What is the approximate value of land purchased for $30,000 that appreciates at 5% per year after 51 years?

Back

The approximate value is $30,000(1.05)^51, which is about $344,022.

Tags

CCSS.HSF.BF.A.2

Front

What does it mean if a quantity is said to be in decay?

Back

It means that the quantity is decreasing over time, often modeled by an exponential decay function.

Tags

CCSS.HSF-IF.C.8B