Answer: Choice B
f(x) = 18(6/5)^x
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Explanation:
When x = 0, we have y = 18. The y intercept value is 18. This is the initial value, and it's the value of 'a' in the equation below
y = a*b^x
The value of b is tied to the growth or decay rate, depending on if b > 1 or if 0 < b < 1 respectively.
In this case, we have growth due to y increasing as x increases. They increase together.
When x increases by 1 like this, the value of b can be determined by dividing any y term over its previous value. So for instance, we can say b = 21.6/18 = 1.2 or we could say b = 25.92/21.6 = 1.2
Then note how 1.2 = 6/5, which means b = 6/5
Therefore, y = a*b^x becomes y = 18(6/5)^x
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We can confirm this equation by plugging in x values from the table and we should get the y values, or f(x) values, listed
Example: plug in x = 0 to find that
y = 18(6/5)^x
y = 18(6/5)^0
y = 18(1)
y = 18 which matches
Then try x = 1
y = 18(6/5)^x
y = 18(6/5)^1
y = 18(1.2)
y = 21.6 that also matches
I'll let you confirm the other x values.
