To find the function that best models the given data, we can analyze the relationship between the x-values and the y-values given in your table:
x y
0 5
1 15
2 45
3 135
4 405
We notice a pattern in the y-values that suggests a relationship based on powers of 3:
- For x = 0, y = 5, which is basically \(5 \cdot 3^0 = 5\)
- For x = 1, y = 5 \cdot 3^1 = 15
- For x = 2, y = 5 \cdot 3^2 = 45
- For x = 3, y = 5 \cdot 3^3 = 135
- For x = 4, y = 5 \cdot 3^4 = 405
This indicates that the function \(f(x) = 5 \cdot 3^x\) is indeed a good fit for the data provided.
Now let's calculate \(f(-1)\):
\[ f(-1) = 5 \cdot 3^{-1} = 5 \cdot \frac{1}{3} = \frac{5}{3} \]
Thus, from the options:
- f(x) = 5⋅3^x; f(−1)=53
This is the correct choice. Therefore:
f(−1) = \frac{5}{3} or 5/3.