Check In 2 Review

Front

What does the equation A=400(1.23)^x represent?

Back

This equation models exponential growth, where A is the amount of students after x years, starting with 400 students and increasing at a rate of 23% per year.

Front

How do you find the rate of change in an exponential growth model?

Back

The rate of change can be found by calculating the derivative of the function or by identifying the growth factor in the equation.

Front

What is the solution to the system of equations 12x + 15y = 132 and 8x + 11y = 92?

Back

The solution is (1, 5), where x is the cost of adult tickets and y is the cost of children tickets.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases by a constant percentage over time, while exponential decay occurs when a quantity decreases by a constant percentage over time.

Front

What does the function f(x)=2(0.85)^x represent?

Back

This function represents exponential decay, as the base (0.85) is less than 1, indicating a decrease over time.

Front

How do you use substitution to solve a system of equations?

Back

To use substitution, solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be represented by a straight line on a graph, meaning it has a constant rate of change.

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing if its derivative is positive and decreasing if its derivative is negative.

Front

What is the significance of the growth factor in an exponential function?

Back

The growth factor indicates how much the quantity increases or decreases in each time period.