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 is the general form of an exponential growth function?

Back

The general form is f(x) = a * b^x, where b > 1.

Tags

CCSS.HSF-LE.A.1A

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a * b^x, where 0 < b < 1.

Front

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

Back

The base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

Tags

CCSS.HSF-IF.C.8B

Front

What is the y-intercept of an exponential function?

Back

The y-intercept is the value of the function when x = 0, which is f(0) = a.

Tags

CCSS.HSF-IF.C.7E

Front

How do you determine the range of an exponential function?

Back

The range of an exponential function is all real numbers greater than 0 if the function approaches a horizontal asymptote.

Tags

CCSS.HSF-IF.C.7E

Front

What is the horizontal asymptote of an exponential decay function?

Back

The horizontal asymptote is the line that the function approaches but never touches, typically y = 0.

Tags

CCSS.HSF-IF.C.7E

Front

How do you calculate the value of an investment with exponential growth?

Back

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

Front

What does a percentage increase of 5% per year mean in terms of an exponential function?

Back

It means the function can be modeled as f(t) = P(1.05)^t, where P is the initial amount.

Front

What is the difference between exponential growth and linear growth?

Back

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

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9