Evaluate the function. Round your answer to four decimal places, if necessary. \( f(x)=2.4(4)^{-x+1}+2.2 \), for \( f(-2) \) \( f(-2)= \)

To evaluate the function \( f(x)=2.4(4)^{-x+1}+2.2 \) for \( f(-2) \), we first substitute \( -2 \) for \( x \): \[ f(-2) = 2.4(4)^{-(-2)+1} + 2.2 \] This simplifies to: \[ f(-2) = 2.4(4)^{3} + 2.2 \] Now, calculate \( 4^{3} \): \[ 4^{3} = 64 \] Then, substitute back: \[ f(-2) = 2.4(64) + 2.2 \] Calculating \( 2.4 \times 64 \): \[ 2.4 \times 64 = 153.6 \] Now, adding \( 2.2 \): \[ f(-2) = 153.6 + 2.2 = 155.8 \] Therefore, rounded to four decimal places, \[ f(-2) = 155.8000 \]