ANSWER:
a.
b.
[tex]\begin{gathered} f\mleft(0\mright)=\frac{198}{1+4e^{-2\cdot0}}=\frac{198}{1+4}=\frac{198}{5}=39.6 \\ f(10)=\frac{198}{1+4e^{-2\cdot10}}=197.99\cong198 \end{gathered}[/tex]
c. increasing
d. 198
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f\mleft(x\mright)=\frac{198}{1+4e^{-2x}}[/tex]
a.
From the function we can see that the factor with e (euler) when x increases will become smaller, therefore the values of the function will increase, the only graph that meets these characteristics is the following:
b.
We must calculate when x = 0 and when x = 10, like this:
[tex]\begin{gathered} f\mleft(0\mright)=\frac{198}{1+4e^{-2\cdot0}}=\frac{198}{1+4}=\frac{198}{5}=39.6 \\ f(10)=\frac{198}{1+4e^{-2\cdot10}}=197.99\cong198 \end{gathered}[/tex]
c.
The function is increasing since as the values of x increase, the values of y increase
d.
The limiting value for f (x) is 198, since the function will never be able to reach this value because there is a horizontal asymptote at that point
