Question

Which of the following functions represent exponential growth?

Which of the following functions represent exponential decay?

Answer 1

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Answer:

1. a, b, c - represent growth

2. b, c, d - represent decay

Explanation:

If increasing x results in a larger value, the function represents growth. If it results in a smaller value, the function represents decay.

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To answer these questions, you can look at the base and the exponent. When we say "exponent" here, we mean the coefficient of the exponent variable. There are four possibilities:

growth:

• exponent positive, base > 1
• exponent negative, base < 1

decay:

• exponent positive, base < 1
• exponent negative, base > 1

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Growth questions:

1.77^x -- growth

1.5^(x/2) -- growth

0.5^(-x) -- growth (= 2^x)

e^(-t) -- decay (e ≈ 2.718)

Decay questions:

1.7^x -- growth

1.7^(-2x) -- decay

(1/3)^x -- decay (= 3^(-x))

2^(-x) -- decay