To find the formula for the function, let's carefully assemble the information piece by piece and place the given values in their corresponding positions in the function's formula.
The general formula for the function is given by:
[tex]\[ y = a \cdot \cos(b \cdot (x - c)) + d \][/tex]
We are provided with the constants that fit into this formula:
1. The amplitude [tex]\( a \)[/tex] is 14.6.
2. The coefficient [tex]\( b \)[/tex] inside the cosine function is 0.2.
3. The horizontal shift [tex]\( c \)[/tex] is 10.3.
4. The period [tex]\( T \)[/tex] is given by [tex]\( 2\pi \)[/tex], but we notice that it's [tex]\( 2\pi \)[/tex] divided by the coefficient [tex]\( b \)[/tex] in the cosine function.
5. The vertical shift [tex]\( d \)[/tex] is 16.8.
Now let’s correctly place these values into the formula:
[tex]\[ y = 14.6 \cdot \cos(0.2 \cdot (x - 10.3)) + 16.8 \][/tex]
Thus, the complete formula for the function is:
[tex]\[ y = 14.6 \cdot \cos(0.2 \cdot (x - 10.3)) + 16.8 \][/tex]
This is the detailed step-by-step construction of the function based on the given values.
