State whether the equation represents exponential growth, exponential

Answered question

2022-02-03

State whether the equation represents exponential growth, exponential decay,f(x)=14⋅12x

Answer & Explanation

karton

karton

Expert2023-04-22Added 613 answers

The equation f(x)=1412x represents exponential growth.

To see why, let's first take a look at the general form of an exponential function: f(x)=abx, where a and b are constants.

In our given equation, we have a = 14 and b = 12. Since b is greater than 1, we know that this function will represent exponential growth. This means that as x increases, the value of f(x) will also increase at an increasing rate.

To understand this intuitively, consider plugging in a few values for x:

- When x = 0, we have f(0)=14120=14
- When x = 1, we have f(1)=14121=168. This is much larger than f(0), which makes sense since we're seeing exponential growth. 
- When x = 2, we have f(2)=14122=2016. Again, this is much larger than f(1), which is larger than f(0).

So, we can conclude that the given equation represents exponential growth.

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