Topics 5-6 Algebra 1 Review (Envision)

Front

What is the formula for exponential growth?

Back

f(x) = a(1 + r)^x, where 'a' is the initial amount and 'r' is the growth rate.

Tags

CCSS.HSF-IF.C.8B

Front

How do you calculate the average rate of change?

Back

Average rate of change = (f(b) - f(a)) / (b - a), where [a, b] is the interval.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage.

Front

What does it mean for a function to have a constant rate of change?

Back

A function has a constant rate of change if the difference in output values is the same for equal intervals of input.

Tags

CCSS.HSF-LE.A.1B

Front

How do you model a situation with exponential growth?

Back

Use the formula y = a(1 + r)^x, where 'a' is the starting value and 'r' is the growth rate.

Tags

CCSS.HSF-LE.A.1A

Front

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

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for calculating percentage increase?

Back

Percentage Increase = [(New Value - Original Value) / Original Value] * 100.

Tags

CCSS.6.RP.A.3C

Front

How do you interpret the slope of a linear function?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Tags

CCSS.8.EE.B.5

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 and 'b' is a positive real number.

Front

What does it mean for a temperature change to be at an exponential rate?

Back

It means that the temperature increases by a percentage of its current value over equal time intervals.