Writing Exponential Functions from Word Problems

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 model exponential growth?

Back

A function models exponential growth if the base 'b' is greater than 1, indicating that the quantity increases over time.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

A function models exponential decay if the base 'b' is between 0 and 1, indicating that the quantity decreases over time.

Tags

CCSS.HSF-IF.C.8B

Front

How do you write an exponential function for depreciation?

Back

For depreciation, the function is written as y = initial_value * (1 - rate)^t, where 'rate' is the depreciation rate and 't' is time.

Front

How do you write an exponential function for growth?

Back

For growth, the function is written as y = initial_value * (1 + rate)^t, where 'rate' is the growth rate and 't' is time.

Tags

CCSS.HSF.LE.A.2

Front

What is the formula for calculating the amount after exponential growth?

Back

The formula is 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 time.

Front

What is the formula for calculating the amount after exponential decay?

Back

The formula is A = P(1 - r)^t, where A is the amount after time t, P is the principal amount, r is the decay rate, and t is time.

Front

If a car's value is $20,000 and it depreciates at 10% per year, what is the exponential function?

Back

y = 20,000(0.90)^t.

Tags

CCSS.HSF.LE.A.2

Front

If a population of bacteria triples every hour, how is this represented in an exponential function?

Back

f(h) = initial_population * (3^h).

Tags

CCSS.HSF.LE.A.2

Front

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

Back

The base determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B