To determine which function represents the same relationship as the points given in the table, we look for a function of the form \( y = ab^x \), where \( a \) is a constant and \( b \) is the base of the exponential function.
Given your points:
- At \( x = 0 \), \( y = 21 \). This indicates that \( a = 21 \) because \( y = ab^0 = a \).
- With the other points, we can use them to find \( b \).
Let's take two points to find \( b \). Using the points \( (0, 21) \) and \( (1, 26.25) \):
- \( y(0) = 21 = ab^0 \to 21 = 21 \)
- \( y(1) = 26.25 = 21b \)
From the second point, solve for \( b \):
\[ 21b = 26.25 \ b = \frac{26.25}{21} \approx 1.25 \]
Now, check the next points to confirm that this works for all of them.
Using \( a = 21 \) and \( b \approx 1.25\):
- \( y(2) = 21(1.25^2) = 21(1.5625) \approx 32.8125 \) (matches)
- \( y(3) = 21(1.25^3) = 21(1.953125) \approx 41.015625 \) (matches)
Now that we have confirmed the values:
The function that represents this relationship is approximately \( y = 21(1.25)^x \).
Without the specific choices (A, B, C, D), you can check for this function form among those options to identify the correct one. If one of the options is \( y = 21(1.25)^x \), that is your answer.
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