Exponential Word Problems

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What is an exponential function?

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An exponential function is a mathematical function of the form f(x) = a * b^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.

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What is the formula for compound interest?

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The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years the money is invested or borrowed.

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How do you calculate exponential growth?

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Exponential growth can be calculated using the formula A = Pe^(rt), where A is the amount after time t, P is the initial amount, e is the base of the natural logarithm, r is the growth rate, and t is time.

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How do you calculate exponential decay?

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Exponential decay can be calculated using the formula A = Pe^(-rt), where A is the amount after time t, P is the initial amount, e is the base of the natural logarithm, r is the decay rate, and t is time.

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What is the doubling time in exponential growth?

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The doubling time is the time required for a quantity to double in size or value. It can be calculated using the rule of 70: Doubling Time (in years) = 70 / growth rate (as a percentage).

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What is the half-life in exponential decay?

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Half-life is the time required for a quantity to reduce to half its initial value. It is commonly used in radioactive decay and can be calculated using the formula: Half-life = ln(2) / decay rate.

Front

If a population of 1,000 increases by 20% each year, what will be the population after 3 years?

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Population after 3 years = 1000 * (1 + 0.20)^3 = 1,728.

Tags

CCSS.HSF-LE.A.1C

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If a bacteria culture starts with 200 bacteria and doubles every 4 hours, how many bacteria will there be after 16 hours?

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After 16 hours, the population will be 200 * 2^(16/4) = 3,200 bacteria.

Tags

CCSS.HSF.LE.A.4

Front

What is the difference between linear and exponential growth?

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Linear growth increases by a constant amount over equal time intervals, while exponential growth increases by a percentage of the current amount, leading to faster growth as the quantity increases.

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How do you solve an exponential equation?

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To solve an exponential equation, you can take the logarithm of both sides, which allows you to bring down the exponent and solve for the variable.