Given the function
[tex]C(t)=235-105e^{(-0.3t)}[/tex]where t is time measured in months.
a) The initial cholesterol level occurs when t=0; therefore,
[tex]\begin{gathered} C(0)=235-105e^{(-0.3\cdot0)}=235-105\cdot1=130 \\ \Rightarrow C(0)=130 \end{gathered}[/tex]The answer to part (a) is 130 mg/dL
(b) After three months, t=3, and the cholesterol level will be
[tex]C(t=3)=C(3)=235-105e^{(-0.3\cdot3)}[/tex]After calculations
[tex]\Rightarrow C(3)=235-105e^{(-0.9)}=192.3102\ldots\approx192.31[/tex]Then, after three months, the amount of cholesterol in the blood will be 192.31 mg/dL.
(c)
[tex]\begin{gathered} C(5)=235-105e^{(-0.3\cdot5)}=235-105e^{-1.5}=211.5713\ldots\approx211.57 \\ \Rightarrow C(5)\approx211.57 \end{gathered}[/tex]The answer to part (c) is C(5)=211.57 mg/dL, and C(5) is the amount of cholesterol in the blood after 5 months.