Question
Which equation represents exponential growth? (1 point) O f(x) = 2 * (3) ^ x; f(x) = 3 * (0.11) ^ x O f(x) = 2 * (1/2) ^ x O f(x) = 5(1/6 ^ x)
Answers
Answered by
GPT-4o mini
The equation that represents exponential growth is:
**f(x) = 2 * (3) ^ x**
In this equation, the base of the exponent (3) is greater than 1, which indicates that the function will increase exponentially as x increases.
The other equations represent exponential decay:
- f(x) = 3 * (0.11) ^ x (base 0.11 < 1)
- f(x) = 2 * (1/2) ^ x (which can be written as f(x) = 2 * (2 ^ -1) ^ x = 2 * (2 ^ -x), base 1/2 < 1)
- f(x) = 5(1/6 ^ x) (which can be written as f(x) = 5 * (6^-1) ^ x = 5 * (6^-x), base 1/6 < 1)
Therefore, the correct choice representing exponential growth is **f(x) = 2 * (3) ^ x**.
**f(x) = 2 * (3) ^ x**
In this equation, the base of the exponent (3) is greater than 1, which indicates that the function will increase exponentially as x increases.
The other equations represent exponential decay:
- f(x) = 3 * (0.11) ^ x (base 0.11 < 1)
- f(x) = 2 * (1/2) ^ x (which can be written as f(x) = 2 * (2 ^ -1) ^ x = 2 * (2 ^ -x), base 1/2 < 1)
- f(x) = 5(1/6 ^ x) (which can be written as f(x) = 5 * (6^-1) ^ x = 5 * (6^-x), base 1/6 < 1)
Therefore, the correct choice representing exponential growth is **f(x) = 2 * (3) ^ x**.
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