Q2: Pre-AP Algebra 2 Retake on Flashcard#1 for Unit 1: L1.4-L1.5

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What is the formula for exponential decay?

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The formula for exponential decay is given by: P(t) = P0 * e^(-kt), where P0 is the initial quantity, k is the decay constant, and t is time.

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How do you calculate the future value of an investment with compound interest?

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The future value (FV) can be calculated using the formula: FV = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

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

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The base in an exponential function determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

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How do you interpret the parameters in the function T = 12,000(1.03)^x?

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In the function T = 12,000(1.03)^x, 12,000 is the initial tuition, 1.03 is the growth factor (indicating a 3% increase), and x represents the number of years since the college opened.

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What is the formula for calculating percentage decrease?

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The formula for calculating percentage decrease is: Percentage Decrease = ((Original Value - New Value) / Original Value) * 100.

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How do you find the population after a certain number of years with a percentage decrease?

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To find the population after a certain number of years with a percentage decrease, use the formula: P(t) = P0 * (1 - r)^t, where P0 is the initial population, r is the rate of decrease, and t is the number of years.

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What is the concept of compound interest?

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Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

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How do you calculate the total amount in a savings account after a certain number of years?

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To calculate the total amount in a savings account after a certain number of years, use the formula: A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

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What does the term 'exponential growth' mean?

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Exponential growth refers to an increase that occurs at a rate proportional to the current value, resulting in the quantity growing faster as it becomes larger.

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How do you determine the tuition in a future year using an exponential function?

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To determine the tuition in a future year using an exponential function, substitute the number of years since the base year into the function and solve for T.