FIAB Creating Equations

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What is an exponential decay function?

Back

An exponential decay function describes a process where a quantity decreases at a rate proportional to its current value, often represented as y = a * e^(-kt), where 'a' is the initial amount, 'k' is the decay constant, and 't' is time.

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How do you calculate total earnings with hourly wage and commission?

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Total earnings = (Hourly wage * Hours worked) + (Commission rate * Total sales). For example, if you earn $10/hour and 5% commission on $6,380 in sales, your total earnings would be $10*35 + 0.05*6380.

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What is an inequality?

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An inequality is a mathematical statement that compares two expressions, showing that one is less than, greater than, less than or equal to, or greater than or equal to the other, often represented with symbols like <, >, ≤, or ≥.

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How do you write an equation for total revenue from ticket sales?

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To write an equation for total revenue, multiply the number of each type of ticket sold by its price and sum them up. For example, T = (number of student tickets * price of student ticket) + (number of adult tickets * price of adult ticket).

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What does the variable 'X' represent in equations?

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In equations, 'X' typically represents an unknown quantity that you are trying to solve for, such as the number of items purchased or the value of a variable.

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What is the formula for calculating total sales from commission and earnings?

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Total sales = (Total earnings - (Hourly wage * Hours worked)) / Commission rate.

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What is the significance of the decay constant in exponential decay?

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The decay constant (k) determines the rate at which the quantity decreases; a larger k means a faster decay.

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How do you set up an inequality for a budget constraint?

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To set up an inequality for a budget constraint, express the total cost of items in terms of variables and set it less than or equal to the budget. For example, if each item costs $2 and the budget is $30, the inequality would be 2X ≤ 30.

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What is the difference between a linear equation and an inequality?

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A linear equation shows a relationship where two expressions are equal, while an inequality shows a relationship where one expression is not equal to the other, indicating a range of possible values.

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How do you interpret the solution of an inequality?

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The solution of an inequality represents a range of values that satisfy the condition. For example, if 2X < 30, the solution indicates all values of X that are less than 15.