Exponential Growth Functions Exit Ticket 11/19

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What is an exponential growth function?

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An exponential growth function is a mathematical function of the form f(x) = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time period.

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What does the term 'initial value' refer to in an exponential function?

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The initial value is the starting amount or quantity in an exponential function, represented by 'a' in the function f(x) = a(1 + r)^x.

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How do you express exponential growth in terms of doubling time?

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Exponential growth can be expressed in terms of doubling time using the formula: Amount = Initial Amount * 2^(t/T), where 't' is the time elapsed and 'T' is the doubling time.

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What is the formula for calculating the future value of an investment with compound interest?

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The future value (FV) of an investment with compound interest is 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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How do you calculate the value of an item after a certain number of years with a fixed percentage increase?

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To calculate the value of an item after a certain number of years with a fixed percentage increase, use the formula: Future Value = Present Value * (1 + r)^t, where r is the rate of increase 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 growth rate; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

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How do you determine the total amount after a certain number of years with continuous compounding?

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The total amount with continuous compounding is calculated using the formula: A = Pe^(rt), where A is the amount, P is the principal, e is Euler's number (approximately 2.718), r is the interest rate, and t is the time in years.

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What is the difference between simple interest and compound interest?

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Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any interest that has been added to it.

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How can you represent exponential growth in a real-world scenario?

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Exponential growth can be represented in scenarios such as population growth, investment growth, and the spread of diseases, where quantities increase rapidly over time.

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What is the formula for calculating the value of a home that appreciates at a fixed percentage annually?

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The formula for calculating the future value of a home that appreciates at a fixed percentage annually is: Future Value = Present Value * (1 + r)^t, where r is the annual appreciation rate and t is the number of years.