hms Exponential Functions - WORD PROBLEMS

Front

What is the general form of an exponential function?

Back

f(x) = a ⋅ b^x, where a is the initial value and b is the base.

Tags

CCSS.HSF.LE.A.2

Front

What does the variable 'a' represent in the exponential function f(x) = a ⋅ b^x?

Back

The initial value of the function.

Tags

CCSS.HSF-IF.C.8B

Front

What does the base 'b' indicate in an exponential function?

Back

If b > 1, it indicates exponential growth; if 0 < b < 1, it indicates exponential decay.

Tags

CCSS.HSF-IF.C.8B

Front

How can you determine if an exponential function represents growth or decay?

Back

If the base b is greater than 1, it represents growth; if b is between 0 and 1, it represents decay.

Tags

CCSS.HSF-IF.C.8B

Front

Write the equation for a population that starts at 200 and grows by 5% each year.

Back

y = 200(1.05)^x.

Tags

CCSS.HSF.LE.A.2

Front

If a quantity decreases by 20% each year, what is the decay factor?

Back

The decay factor is 0.8.

Tags

CCSS.HSF-LE.A.1C

Front

What is the equation for a culture of bacteria that starts with 1000 cells and dies by 25% each year?

Back

y = 1000(0.75)^x.

Tags

CCSS.HSF.LE.A.2

Front

In the context of exponential functions, what does the term 'half-life' refer to?

Back

The time required for a quantity to reduce to half its initial value.

Front

How do you express the number of teams remaining after r rounds if half are eliminated each round starting with 128 teams?

Back

t = 128(0.5)^r.

Tags

CCSS.HSF.LE.A.2

Front

What is the relationship between exponential functions and logarithms?

Back

Logarithms are the inverse operations of exponential functions.

Tags

CCSS.HSF.BF.B.5