To determine the initial amount Andy deposited into his savings account, we need to evaluate the function [tex]\( f(x) \)[/tex] at [tex]\( x = 0 \)[/tex].
The piecewise function is defined as follows:
[tex]\[
f(x)=\left\{\begin{array}{ll}
40 x+550, & 0 \leq x<5 \\
750, & 5 \leq x<8 \\
750+80(x-8), & 8 \leq x<10
\end{array}\right.
\][/tex]
We are asked to find the initial amount, which corresponds to [tex]\( f(0) \)[/tex]. According to the definition of the piecewise function, for [tex]\( 0 \leq x < 5 \)[/tex], the function is [tex]\( f(x) = 40x + 550 \)[/tex].
Substituting [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = 40(0) + 550 = 550
\][/tex]
Therefore, the initial amount Andy deposited into his savings account is [tex]\( \$550 \)[/tex].
The correct answer is:
[tex]\[
\$550
\][/tex]
