Question

A b C the amount of cholesterol c =c (T)

Answer 1

Given the function

`C(t)=235-105e^((-0.3t))`

where t is time measured in months.

a) The initial cholesterol level occurs when t=0; therefore,

`\begin{gathered} C(0)=235-105e^((-0.3\cdot0))=235-105\cdot1=130 \\ \Rightarrow C(0)=130 \end{gathered}`

The answer to part (a) is 130 mg/dL

(b) After three months, t=3, and the cholesterol level will be

`C(t=3)=C(3)=235-105e^((-0.3\cdot3))`

After calculations

`\Rightarrow C(3)=235-105e^((-0.9))=192.3102\ldots\approx192.31`

Then, after three months, the amount of cholesterol in the blood will be 192.31 mg/dL.

(c)

`\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}`

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.