Question

the number of residents of a certain state (in thousands) who are enrolled in medicare t years since 2000 can be represented by the equation M=82t +2715

Answer 1

a) To find the M-intercept, we will fix the t value at 0 thus:

$\begin{gathered} M=82t+2715 \\ AT\text{ t=0} \\ M=82(0)+2715 \\ M=2715 \end{gathered}$

The m-intercept is:

(t,M) = (0,2715)

The explanation is:

In the year 2000, the state had 2715 thousand residents enrolled in Medicare.

b) To find the t-intercept, we will fix M at 0 in the equation thus:

$\begin{gathered} M=82t+2715 \\ 0=82t+2715 \\ -2715=82t \\ \frac{-2715}{82}=\frac{82t}{82} \\ -33.1098=t \\ -33.1(to\text{ 1 d.p) =t} \end{gathered}$

The t-intercept is:

(t,M) = (-33.1,0)

The explanation is:

Since t is -33.1, but to the nearest integer, t = -33

The year will be 2000-33 = 1967

So, therefore:

In the year 1967, the state had 0 thousand residents enrollled in Medicare.