Samantha works in a bakery. The profit of cupcakes in dollars, after [tex]t[/tex] weeks, is given by the function [tex]C(t)=0.1 t^3[/tex]. The profit of cookies in dollars, after [tex]t[/tex] weeks, is given by the function [tex]K(t)=5(1.07)^t-5[/tex].

Which function describes the total profit, [tex]M(t)[/tex], at the bakery after [tex]t[/tex] weeks?

A. [tex]M(t)=0.1 t^3+5(1.07)^t-5[/tex]
B. [tex]M(t)=0.1 t^3+5(1.07)^t+5[/tex]
C. [tex]M(t)=10 t^3+5(1.07)^t-5[/tex]
D. [tex]M(t)=0.1 t^3-5(1.07)^t-5[/tex]



Answer :

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]