To determine the total profit, [tex]\( M(t) \)[/tex], at the bakery after [tex]\( t \)[/tex] weeks, we need to sum the profit from cupcakes and the profit from cookies.
Given:
- The profit function for cupcakes is [tex]\( C(t) = 0.1 t^3 \)[/tex].
- The profit function for cookies is [tex]\( K(t) = 5(1.07)^t - 5 \)[/tex].
The total profit, [tex]\( M(t) \)[/tex], is the sum of these two functions:
[tex]\[ M(t) = C(t) + K(t) \][/tex]
[tex]\[ M(t) = (0.1 t^3) + (5(1.07)^t - 5) \][/tex]
Combining the terms, the total profit function is:
[tex]\[ M(t) = 0.1 t^3 + 5(1.07)^t - 5 \][/tex]
Therefore, the function that describes the total profit, [tex]\( M(t) \)[/tex], at the bakery after [tex]\( t \)[/tex] weeks is:
[tex]\[ M(t) = 0.1 t^3 + 5(1.07)^t - 5 \][/tex]
The correct answer is:
[tex]\[ \boxed{M(t) = 0.1 t^3 + 5(1.07)^t - 5} \][/tex]
