Alg Module 13 Flashcard

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = ab^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It describes growth or decay processes.

Front

What does it mean for a population to decrease by a percentage each year?

Back

It means that each year, the population is reduced by that percentage of its current size. For example, a 1.5% decrease means that each year, the population is multiplied by (1 - 0.015).

Front

How do you write a linear equation for total cost?

Back

A linear equation for total cost can be written as c = mx + b, where 'm' is the cost per unit, 'x' is the number of units, and 'b' is the fixed cost.

Front

What is the formula for calculating the total cost of renting equipment?

Back

The total cost can be calculated using the formula c = fixed cost + (variable cost per unit * number of units).

Front

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

Back

The base determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if it is between 0 and 1, it represents exponential decay.

Front

How do you determine the equation from a table of values?

Back

To determine the equation from a table, identify the relationship between the variables, check for linearity or exponential patterns, and use points to derive the equation.

Front

What does the term 'fixed cost' refer to in a cost equation?

Back

Fixed cost refers to a cost that does not change with the level of output or activity, such as rental fees or initial charges.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage, leading to faster growth over time.

Front

How can you represent a decrease in population mathematically?

Back

A decrease in population can be represented using an exponential decay function, such as y = initial population * (1 - rate)^t.

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.